The bipartisan compromise is encouraging, but several questions remain, said Norm Ornstein, a longtime political analyst and co-author of "It's Even Worse Than It Looks: How the American Constitutional System Collided with the New Politics of Extremism.

"One, will this compromise make it through the Senate, once the details are hammered out (always more difficult than frameworks) and with a lot more than 60 votes? Two, will House Republicans, who have very different impulses and constituencies, be supportive? Three, if not, will (House Speaker John) Boehner bring an immigration bill to the floor that will get many more Democratic votes than Republican?" Ornstein said.

Other Senate-led bipartisan efforts have faced similar chances of success.

Proposals to resolve the debt crisis -- including the so-called super committee -- failed. The nation was able to avert the fiscal cliff narrowly thanks, in part, to the bipartisan efforts of Senate Minority Leader Mitch McConnell and Vice President Joe Biden.

But political experts said that on immigration, there might be more room to meet in the middle.

Still, for his part, Boehner was noncommittal.

"The speaker welcomes the work of leaders like Sen. Rubio on this issue, and is looking forward to learning more about the proposal in the coming days," Boehner spokesman Michael Steel said.