WASHINGTON — Undocumented immigrants would be able to seek legal status without first going home under a compromise framework floated Monday by a bipartisan group of senators, according to a source familiar with the plan.

The outline for a possible immigration reform bill reflects a mainstream Republican willingness to compromise on what President Barack Obama calls a top priority of his second term.

However, conservatives immediately voiced their opposition to providing undocumented immigrants a path to legal status, especially in the Republican-led House.

One House Republican labeled the senators’ plan as “amnesty” — a politically loaded word that seeks to ensure conservative rejection.

Obama won re-election in November with strong support from Latinos, the fastest-growing demographic.

That has caused GOP leaders to seek a deal with Democrats that would provide a path to legal status for many of the nation’s 11 million undocumented immigrants — an outcome long opposed by conservatives as amnesty.

“There is a new, I think, appreciation on both sides of the aisle — including maybe more importantly on the Republican side of the aisle — that we have to enact a comprehensive immigration reform bill,” Sen. John McCain, R-Arizona, said Sunday.

“We are losing dramatically the Hispanic vote, which we think should be ours, for a variety of reasons, and we’ve got to understand that,” McCain told ABC’s “This Week.”

McCain is one of the eight senators proposing the compromise. Four are influential Democrats, while Republicans joining McCain in the effort include tea party backed newcomers Marco Rubio of Florida and Jeff Flake of Arizona — two states where immigration is a major issue.

House Speaker John Boehner’s office was non-commital, saying he looked forward to learning more about the senators’ plan, while conservative Rep. Lamar Smith, R-Texas, rejected it.

“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 Smith, who serves on the immigration subcommittee in the House. “By granting amnesty, the Senate proposal actually compounds the problem by encouraging more illegal immigration.”

NumbersUSA, a group seeking to reduce U.S. immigration, called the Senate plan an attempt to “out-amnesty Obama” and said it was activating its 1.3 million members to push for congressional opposition.

The senators will announce their plan a day before Obama speaks in Las Vegas on immigration reform, signaling a major push by both sides to focus on the contentious issue in the new Congress.

Aides say the president’s remarks on Tuesday will touch on the blueprint he’s detailed in the past: improving border security, cracking down on employers who hire undocumented workers, and creating a pathway to “earned” citizenship for undocumented immigrants.

Those provisions align closely with what the eight senators laid out in a framework of their legislation, which was obtained by CNN on Sunday.

The legislators based the proposal on four “pillars.” These include:

— A “tough but fair” path to citizenship for undocumented immigrants already living in the United States, after bolstering the nation’s border security;

— Overhauling the country’s legal immigration system, including attaching green cards to advanced degrees in science, technology, engineering, or math from U.S. universities;

— Establishing an employment verification system that holds employers accountable for hiring undocumented workers;

— Creating a guest worker program for positions that Americans are either unable or unwilling to fill.

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. Republican Lindsey Graham of South Carolina rounds out the overall group.

Menendez said the time was right for pushing major immigration reform through the Senate.

“First of all, Americans support it in poll after poll,” he said. “Secondly, Latino voters expect it. Thirdly, Democrats want it. And fourth, Republicans need it.”

A source familiar with how the eight senators came up with the plan told CNN that Graham called Schumer after the November vote to restart work on an immigration bill that broke down in 2010.

Soon, a core group of six senators formed and met five times in the following weeks in the offices of Schumer and McCain, the source said, adding that Flake and Bennet also took part in some of the meetings and were the last to agree to the proposal.

An initial timetable by the senators called for a framework by the end of January, the text of a bill to to the Senate Judiciary Committee by March, and Senate passage by the end of July, according to the source.

The group last met on Wednesday, then worked through some details before Schumer called Obama on Sunday to tell him of Monday’s planned announcement, the source said.

While specifics on border security and legal status for undocumented immigrants need to be worked out, the framework lacks any requirement for people in the United States illegally to return to their home countries before getting a shot at legal status, according to the source.

Obama came under criticism from Latino activists for failing to deliver on 2008 campaign promise to make immigration reform a priority of his first term.

Last year, as his re-election campaign heated up, 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 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.

Since the election, mainstream Republican leaders and some conservatives such as Rubio, a child of Cuban immigrants and considered a rising star in the party, have called for addressing the immigration issue instead of ceding the Latino vote to Democrats.

McCain, a veteran of failed attempts to address the issue during the George W. Bush administration, said the senators’ proposal wasn’t “that much different from what we tried to do in 2007.”

Obama met behind closed doors Friday with members of the Congressional Hispanic Caucus and vowed to “move the debate forward,” the White House said in a statement. Rep. Xavier Becerra , D-California, who was at the meeting, said that Obama had indicated that immigration reform “is his top legislative priority.”

— CNN’s Kevin Liptak, Catherine Shoichet and Matt Smith contributed to this report.