Rep. Luis Gutierrez, D-Ill., said this week 40 or 50 GOP representatives support proposed reforms, The Washington Post reported.
He characterized Republican supporters as saying "Love to do the activity with you. I want to be able to vote for it. I really don't need to draw attention to myself at this point."
Gutierrez said President Obama asked him in 2009 to find "40 or 50 Republicans" who could support immigration reform.
"I know where they're at," he said. "They're here. They're present."
He said a bill under consideration in the House has the support of at least 195 Democrats. Votes from 23 Republicans would be needed to pass it if Speaker John Boehner did not enforce the "Hastert Rule," which prevents a measure from being brought to the floor without the support of a majority of the Republican caucus.
The congressman predicted only a few House Democrats would vote against a bill that provides a pathway to citizenship for the estimated 11 million illegal immigrants in the United States, The Hill reported.
Only three Democrats supported legislation earlier this year that would have required the deportation of illegal immigrants brought to the United States as children, Gutierrez added.