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WASHINGTON (CNN) -- President Barack Obama has invited congressional leaders to the White House on Wednesday to discuss the need to reopen the government and raise the federal debt ceiling, according to the White House and a spokesman for House Speaker John Boehner.

The meeting comes on the second day of a government shutdown caused by a stalemate over the insistence of House Republicans to include provisions to dismantle or delay Obamacare with a short-term spending measure needed to fund the government in the new fiscal year that started Tuesday.

Boehner and other Republicans have complained that Obama and Democrats refuse to negotiate on the health care reforms, which expanded this week when government exchanges to purchase private health coverage opened on Tuesday.

Brendan Buck, a spokesman for Boehner, confirmed the Obama meeting was set for 5:30 p.m. ET.

"We're pleased the president finally recognizes that his refusal to negotiate is indefensible," Buck said. "It's unclear why we'd be having this meeting if it's not meant to be a start to serious talks between the two parties."

Obama and his party accuse Republicans of trying to extort them into defunding or delaying Obamacare by using as leverage the need to fund the government and increase the Treasury's capacity to borrow money to pay U.S. bills.

A White House official signaled Obama's opposition to negotiating amid a government shutdown remained unchanged, saying the president's message at his meeting with House and Senate leaders will be for Congress to pass a "clean" funding plan and debt ceiling measure with no Obamacare provisions attached.

Shutdown means furloughs for up to 800,000

With up to 800,000 federal workers facing life without a paycheck, the GOP-led House planned new votes Wednesday on piecemeal spending measures that would fund specific popular programs such as veterans affairs and national parks.

The incremental approach pushed by tea party conservatives led by Sen. Ted Cruz of Texas seeks to put pressure on Democrats to approve spending for programs that Republicans like, but not Obamacare.

An initial effort Tuesday failed because the short-term proposals comprising a tiny portion of the overall federal budget lacked the necessary two-thirds majority support due to Democratic opposition. The next votes will only require majority support.

Senate Majority Leader Harry Reid derided the latest House tactic as "just another wacky idea by tea party Republicans" and the White House has promised a veto.

In a sign of the political pressure involved, Cruz said Wednesday at a committee hearing on intelligence services the shutdown meant widespread furloughs that could compromise national security.

He called for passing a spending measure just for the intelligence agencies, saying "the only impediment to doing so is the prospect that Majority Leader Harry Reid would object to doing so."

However, Democratic Rep. Louise Slaughter of New York said the easier solution was for the House to approve the spending proposal for the entire government sent over by the Senate, which lacks any of the anti-Obamacare provisions demanded by Cruz and his allies.

Political costs increase

The political cost of the shutdown increased Wednesday when Obama canceled planned visits next week to Malaysia and the Philippines as part of an Asian swing that will include a summit of the Association of Southeast Asian Nations on Bali. Obama will still attend the ASEAN summit, his office said.

On Tuesday, the president lambasted the Republicans for being "reckless" in their willingness to have the government shut down if they don't get steps to delay or dismantle his signature health care reforms that the Supreme Court upheld last year.

Saying the shutdown's goal is to hinder government efforts to provide health insurance to 15% of the U.S. population that doesn't have coverage, Obama added it was "strange that one party would make keeping people uninsured the centerpiece of their agenda."

Meanwhile, Reid indicated he was open to working with the House on budgetary matters -- "but not with the government closed" and not by making it all about the health law.

First shutdown in nearly 18 years

The latest shutdown was not the first for the government. The last time it happened, almost 18 years ago during the Clinton administration, the stalemate lasted 21 days.

Now, the House and Senate have both refused to budge from their visions for the budget and, beyond that, health care reform.

Also looming is the October 17 deadline to raise the debt ceiling. Obama and congressional leaders all say that no one wants the stalemate to spread to that issue, which could mean a U.S. default. But no progress has occurred on finding a solution.

Writing Tuesday in USA Today, Boehner dug in his heels on the debt ceiling issue, saying "there is no way Congress can or should pass such a bill without spending cuts and reforms to deal with the debt and deficit."

Obama offered no indication that he'll budge. Noting that such Republican brinkmanship in 2011 led to the first-ever downgrade of the U.S. credit rating, he said Tuesday he "will not negotiate over Congress' responsibility to pay bills it's already racked up."

To CNN Chief National Correspondent John King, it amounts to a stalemate over the dangerous prospect of American defaulting on its debt.

"You have bipartisan consensus among economists that it would be a disaster, a catastrophe, but, politically, you have a divide," King said.

One problem is that conservative House Republicans from home districts with no realistic Democratic challenge feel emboldened to pursue a more extremist ideology backed by their supporters, he said.

"More people say raise the debt ceiling and fight the health care debate somewhere else," King noted. "But there's enough here, if you think of a Republican going home to his district, there's enough here to understand why the Republicans think they're on safe ground dragging this out."

In the House, some moderates are making noise about trying to overcome the conservative hold on strategy over the budget and debt ceiling, but no clear signs have emerged of a shift that might persuade Boehne and other House leaders to change course.

"Both sides have dug in," GOP Rep. Michael Grimm of New York told CNN. "The Democrat side won't discuss anything at all. They won't even have a discussion. Republicans are now in a position where they don't want to cave in because it sets a bad precedent that the Senate would be somewhat dictating how the House runs."

Grimm called for Obama to "stop giving speeches and taking sides at all."

"There is a strong possibility if they were willing to sit down and listen to us that we would put a package together and solve the problems at once, so we can get the government funded, stop the shutdown, and also deal with the debt ceiling so we don't have another crisis a week or two away from now," he said.

Rep. Steny Hoyer of Maryland, the No. 2 Democrat in the House, told CNN that "we may be getting to a place where they're going to be enough rational Republicans to join with the Democrats" and pass a short-term spending plan to reopen the government and allow for broader talks on funding for the rest of the new fiscal year.

Calling that a "cooling off period," Hoyer criticized the piecemeal spending proposals, noting they had "nothing to do with health care because, finally, they've come to grips with the fact that the responsible action to take is to pass legislation which will fund government."

In recent days, the Democratic-led Senate has rejected four separate House GOP spending proposals that would either delay or defund Obamacare.

One House GOP plan also called for a conference committee, which usually results from competing legislation from the two chambers on major issues, rather than a short-term continuing resolution intended to keep the government running for a few weeks.

Democratic Sen. Dick Durbin of Illinois, a leading liberal voice, told CNN that he is open to negotiations with the House on at least one specific provision of Obamacare -- a tax on medical devices that some in both parties oppose.

However, Durbin echoed the position of Reid that such negotiations must be separated from the spending impasse that has shut down the government.

On the Republican side, Rep. Darrell Issa of California told CNN that he could vote to fund the government for a few days or weeks to provide time for a conference committee to work out a compromise.

'The rest of the country thinks we're crazy'

Obamacare isn't directly tied to funding the government. But it's so unpopular among the Republican tea party conservatives that they want it undercut, if not outright repealed. For instance, this week Republican Rep. Todd Rokita of Indiana called it "the most insidious law known to man."

Both Democrats and Republicans say that a clean spending measure -- with no Obamacare amendments, as urged by the president and his allies -- would pass the House with support from the Democratic minority and moderate Republicans.

So far, Boehner has succumbed to pressure from the tea party right to avoid a vote that would pass something without causing some harm to the health care reforms.

GOP Rep. Peter King of New York said the problem is tea party conservatives such as Cruz who "really care about nothing but their own agenda" who are driving the Republican approach in the House.

"We have people in the conference, I believe, who'd be just as happy to have the government shut down," said King, who has been among the Republican legislators pushing for a "clean" funding bill without anti-Obamacare provisions. "They live in these narrow echo chambers. They listen to themselves and their tea party friends. That keeps them going, forgetting that the rest of the country thinks we're crazy."

Amid the finger-wagging and fulminating, major components of the new health insurance law went into effect on schedule on Tuesday.

"The Affordable Care Act is moving forward. You can't shut it down," said a post on Barack Obama's verified Twitter feed.

A blow to the economy

The shutdown of the government -- the country's largest employer -- isn't happening all at once.

Federal employees who are considered essential will continue working. Those deemed non-essential -- up to 800,000 -- could be furloughed, unsure when they'll be able to work or get paid again.

The shutdown could cost the still-struggling U.S. economy about $1 billion a week in pay lost by furloughed federal workers. And that's only the tip of the iceberg.

While many agencies have reserve funds and contingency plans that would give them some short-term leeway, the economic effect would snowball as the shutdown continued.

The total economic impact is likely to be at least 10 times greater than the simple calculation of lost wages of federal workers, said Brian Kessler, economist with Moody's Analytics. His firm estimates that a three- to four-week shutdown would cost the economy about $55 billion.