Party leaders say the harsh language that some Republicans use when discussing illegal immigration has angered many Americans with Hispanic heritages.
Rubio's bipartisan group has proposed legislation to strengthen border security, allow tens of thousands of new high- and low-skilled workers into the country, require all employers to check their workers' legal status, and provide an eventual path to citizenship for some 11 million immigrants now in the country illegally.
Even if the bill survives the Democratic-controlled Senate, stiff resistance is expected in the GOP-dominated House. Many House Republicans dislike the idea of "amnesty" for those who crossed the border illegally, and some say it's foolish to enfranchise likely Democratic voters.
Obama embraces the Rubio plan, and it won crucial praise from House Speaker John Boehner, R-Ohio, and Rep. Paul Ryan, R-Wis., last year's vice presidential nominee.
Rubio and his allies challenge the notion that creating a way to citizenship for millions of people here illegally will dramatically increase Democratic turnout in future elections.
"Not all 11 million illegal immigrants here today will qualify to become citizens, and not all of the 11 million illegal immigrants are Hispanic," according to Rubio's "Myth vs. Fact" website. The site says many immigrants will not choose to become citizens, and many new citizens, like many current ones, will not bother to vote.
Some Republican campaign strategists, however, say the political damage would be worse than party leaders acknowledge.
Republican consultant and pollster Mike McKenna said one of his surveys shows that most Americans favor "immigration reform" and they believe it will benefit Democrats more than Republicans.
In an interview, McKenna said Republican leaders are embracing Rubio's plan without sufficient data on where it might lead. "I think about two months from now, the folks in the establishment are going to wish they hadn't started this conversation," McKenna said.