Conservative Republicans oppose the plan as written because it provides a pathway to citizenship for most of the 11 million immigrants living illegally in the United States.
They call such a move an amnesty for lawbreakers, and they fear the influx of likely Democratic voters in future elections.
In addition, they reject the measure as a "big government" approach that will increase pressure on entitlement programs such as Medicare and Medicaid.
More moderate GOP leaders and legislators believe Republicans risk worse electoral damage if the party is blamed for blocking immigration reform.
In last year's election, Obama won a strong majority of the Hispanic vote in defeating GOP nominee Mitt Romney, and Republican strategists warn of similar results if the party is considered hostile to immigrants.
Conservative Sen. Marco Rubio of Florida, another Republican in the "Gang of Eight," said the alternative to immigration reform was keeping in place a broken system that has led to problems cited by opponents of the legislation.
The first-term senator, who's widely considered a potential 2016 contender for the GOP presidential nomination, told CNN that he's not concerned about the political risk of tying his name so closely to such controversial legislation.
"The easiest thing to do politically is just not deal with the issue -- you know, give a couple speeches, and not play and get involved and try to solve it," Rubio said. "I'm dealing with this because this is hurting our country badly."
Earlier, Vice President Joe Biden made an impassioned appeal for immigration reform on Thursday, telling a prayer breakfast with Latino leaders that "it's time we pass fair -- firm but fair -- reforms to bring these 11 million undocumented immigrants out of the shadows."
Calling the legislation "the morally right thing to do," Biden said "it is not hyperbole in my view to suggest, that for the people we care about, we're at the cusp in our generation of making hope and history rhyme."
A CNN/ORC International poll released this week showed that a solid majority of respondents -- 62% -- think border security should be the main focus of immigration legislation, with 36% saying the legislation should emphasize a path to citizenship for immigrants living illegally in the country.
The poll showed Democrats divided evenly on the question, while independents and Republicans strongly called for a focus on border security.