"Our immigration laws aren't broken, they just aren't enforced," argued Rep. Lamar Smith, R-Texas, after Obama's speech. " ... We've been down this road before with politicians promising to enforce the law in return for amnesty. And then after the amnesty, they fail to make good on the enforcement promises. The American people should not be fooled. 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."

Republican Sen. Mike Lee of Utah objected to the framework by his Senate colleagues, saying the guidelines "contemplate a policy that will grant special benefits to undocumented immigrants based on their unlawful presence in the country."

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 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 added.

Obama, meanwhile, signaled disagreement with Republicans over the state of border security, saying in his speech that the Southwest border was more secure than ever.

He mentioned steps to crack down on the hiring of undocumented workers, as well as unclogging the legal immigration system to encourage highly skilled and educated workers already in the country to remain instead of taking their expertise abroad.

Democratic senators backing the framework unveiled Monday 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.

Meanwhile, U.S. Chamber of Commerce President Tom Donohue has been in talks with Trumka on the issue. He said after Obama's remarks that American business hoped for changes this year.

"We should seize this opportunity to create an immigration system that serves the interests of our economy, our businesses, and our society," Donohue said.

In a sign of the heated public debate on the issue, a group of about two dozen protesters standing across the street from the Las Vegas high school waved signs opposing amnesty for undocument immigrants as Obama's motorcade drove past.