WASHINGTON (CNN) -- President Barack Obama threw his full weight behind a comprehensive overhaul of U.S. immigration laws Tuesday, saying "now's the time" to replace a system he called "out of date and badly broken."
Speaking at a majority-Hispanic high school in Las Vegas, Obama said "a broad consensus is emerging" behind the issue, and "we know where the consensus should be."
"At this moment, it looks like there's a genuine desire to get this done soon. And that's very encouraging," Obama said. "But this time, action must follow we can't allow immigration reform to get bogged down in an endless debate."
He said he framework announced Monday by eight senators -- four from each party -- is "very much in line with the principles I've proposed and campaigned on for the last few years."
With his re-election last November aided by strong support from Latino voters, Obama has made a comprehensive immigration bill a top legislative priority of his second term.
His speech Tuesday was at Del Sol High School, which has a 54% Hispanic student body, according to U.S. News and World Report rankings.
Senior administration officials said before the speech that Obama would not introduce new legislation on Tuesday.
Senators involved in the bipartisan immigration effort said Monday they plan to provide a bill to the Senate Judiciary Committee in March, with hopes of getting the measure passed over the summer
The White House may consider introducing its own legislation if the Senate framework fails to gain traction, according to senior administration officials.
On the House side, a similar effort on immigration is said to be under way involving a group of Republicans and Democrats.
Two senior House Democratic sources briefed on that effort told CNN the group was working to release some sort of outline of its plan soon, possibly as early as this week, but concede "they are not as far along as the Senate."
According to officials briefed on Obama's policy, the president will specify three areas of attention: better enforcement of immigration laws, providing a path to citizenship for the 11 million undocumented immigrants already in the country, and reforming the legal immigration system.
Obama came under criticism from Latino activists for failing to deliver on a 2008 campaign promise to make overhauling immigration policy a priority of his first term.
As his re-election campaign heated up last year, the Obama administration announced a halt to deportations of some young undocumented immigrants in a move that delighted the Latino community.
Exit polls in November indicated that Latino voters gave overwhelming support to Obama over GOP challenger Mitt Romney, who had advocated a policy that amounted to forcing undocumented immigrants to deport themselves.
Under the compromise plan by the senators, millions of undocumented immigrants would get immediate but provisional status to live and work in the United States. The outline also called for strengthening border controls, improved monitoring of visitors and cracking down on hiring undocumented workers.
Only after those steps occurred could the undocumented immigrants already in the country begin the process of getting permanent residence -- green cards -- as a step toward citizenship, the senators said at a news conference.
Florida Sen. Marco Rubio, a tea party-backed conservative considered a rising star in the Republican Party, said the goal of the framework he helped put together was a "modern immigration system" that treated everyone fairly, including those who are undocumented and those waiting to come to America legally.
Speaking on the Senate floor a few hours before Obama's event on Tuesday, Rubio said he hoped the president would embrace the "very common sense and reasonable set of principles" developed by the senators.
"But if his intentions are to trigger a bidding war to see who can come up with the easiest process, this is not a good start," Rubio said.
However, another tea party-backed Republican, Sen. Mike Lee of Utah, objected to the framework by his colleagues, saying the guidelines "contemplate a policy that will grant special benefits to undocumented immigrants based on their unlawful presence in the country."
Other conservatives immediately voiced their opposition to what they called amnesty, a code word on the political right for providing undocumented immigrants a path to legal status.
"When you legalize those who are in the country illegally, it costs taxpayers millions of dollars, costs American workers thousands of jobs and encourages more illegal immigration," said Rep. Lamar Smith, R-Texas, who serves on the immigration subcommittee in the House. "By granting amnesty, the Senate proposal actually compounds the problem by encouraging more illegal immigration."
Rubio rejected such a characterization on Tuesday, saying that the framework would require undocumented immigrants to undergo a background check and face immediate deportation if they committed any serious crimes.
Otherwise, they then would have to pay any back taxes owed as well as a fine to get what Rubio called "the equivalent of a non-resident visa that allows you to work here."
An opportunity to get a green card and possible citizenship would only come after the government undertakes other steps, such as increasing border security, he said.
Members of the Obama administration believe the U.S. border, with an unprecedented 18,000 patrol agents along the Southwest border alone, is currently more secure than ever, so they plan to focus on enforcement inside the country.
Likely steps include strengthening the E-verify system to make it easier for business owners to determine the legal status of potential employees. Officials said the president's plan could include new penalties for businesses that knowingly hire undocumented immigrants.
In addition, the Obama plan would require current undocumented immigrants who clear a background check to learn English, pay fines and back taxes and get in the "back of the line" in applying for eventual citizenship, the officials said.
Other steps would include unclogging the legal immigration system to encourage highly skilled and educated workers already in the country to remain instead of giving up over fighting the system. according to the officials.
Democratic senators backing the plan include Chuck Schumer of New York, Dick Durbin of Illinois, Robert Menendez of New Jersey and Michael Bennet of Colorado. On the Republican side were Rubio, John McCain of Arizona, Lindsey Graham of South Carolina and Jeff Flake of Arizona.
Durbin said Tuesday that immigration reform must have bipartisan support to work, so it won't include everything everyone wants.
"It's going to look different than what I might write, or the president might write," he said.
Like the Senate framework, the House plan will include a path to citizenship, but details of how that will work are still being discussed.
The Senate proposal is a good starting point, Rep. Joe Garcia, D-Florida, said Tuesday on CNN.
"I think it puts us in a very good place," he said.
A litany of left-leaning advocacy groups spoke out on the senators' plan, praising it as a good first step but cautioning against harming the rights of workers.
"The people of this country are ready for us to be one country again without second-class people being mistreated simply because they lack paper, even though they are already contributing to our economy and our tax system," NAACP President Ben Jealous said.
AFL-CIO President Richard Trumka told Yahoo News on Tuesday that his labor federation representing 12 million people will mount a "full-fledged" campaign in support of comprehensive immigration reform.
"We think everybody ought to have the right to work hard and to progress to citizenship," Trumka said.