But Democrats agreed to more border security as Republicans agreed to a pathway to citizenship.

With bipartisan backing from so many high-profile senators, the proposal’s chances of passage look better than ever.

Even if it passes the Senate, the measure will have to go through the more-conservative House, where Miami Republican Rep. Mario Diaz Balart is working on a bipartisan bill in that chamber.

Rubio has close ties to Miami Republican Reps. Ileana Ros-Lehtinen and Balart, who have bucked their own party over immigration and support the effort. So does Rubio’s Florida partner in the Senate, Democrat Bill Nelson. Miami Rep. Joe Garcia, a Democrat, said he welcomed Rubio’s “evolution” on the issue.”

Wisconsin Rep. Paul Ryan, a Republican vice-presidential candidate in the last election, said he, too, supported Rubio’s proposal.

Ryan and his running mate, Republican presidential candidate Mitt Romney, barely earned a quarter of the Hispanic vote, which, in part, cost them the election. Romney’s statement that he favored “self-deportation” of illegal immigrants rubbed many Hispanics the wrong way.

Hispanics, however, began shifting away from the GOP years before as Republicans played a leading role in stopping an immigration reform plan in 2007 backed by McCain, former President Bush and former Florida Sen. Mel Martinez, whose seat Rubio now holds.

McCain said immigration is a “preeminent issue” for Hispanic voters.

“The Republican Party is losing the support of our Hispanic citizens,” McCain said Monday.

Menendez on ABC’s This Week said the speedy timetable shouldn’t be too much of an impediment.

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

The proposal also dovetails with anti-sex trafficking proposals that Rubio backs. He says many sex trafficking victims and witnesses are here unlawfully and are therefore reluctant to cooperate with authorities for fear of deportation.

“It’s not a good idea to have millions of people permanently trapped in an immigration status that keeps them forever at a distance from our society,” Rubio said.