Despite his leading role in pushing immigration reform in 2006 and 2007, the party's 2008 presidential nominee lost the Latino vote, in no small part because the the Republican Party had thwarted reform. McCain took a hard right on immigration policy during his own reelection bid in 2010, before coming back around after the 2012 election.
He said Obama has played a constructive role in reform and has "struck the right balance."
TPM also asked McCain if he believes it's important for Speaker John Boehner (R-OH), who has all but rejected the Senate immigration bill, to stand by his principle that any legislation must have the support of a majority of House Republicans in order to come to a vote.
"I can't tell the Speaker what to do," he said. "I trust him and he's a friend of mine and I have great confidence in his leadership."
McCain responded to GOP operatives' plans to campaign against vulnerable Democratic senators over their immigration reform votes.
"All I can say is that maybe they ought to look back at what happened in 2012 and 2008 with the Hispanic voters and then maybe they ought to reevaluate what they are saying," he said. "There's plenty of issues that separate Republicans and Democrats but ... 70, 80 percent, depending on which polls you judge by, are in favor of what we're trying to do."
The National Republican Senatorial Committee had reportedly indicated that it would target Democrats over the issue, but spokesman Brad Dayspring later denied it and said the NRSC has "no plans" to do so. But he said he believes some Democrats may be hurt by it politically. Fourteen Republicans joined all 54 Democrats in voting for the bill Thursday. All the opposition came from Republican senators.
Recalling the "very bitter disappointment" surrounding the failed reform effort in 2007, McCain sounded a note of confidence that his efforts will bear fruit this time around.
"I am confident the will of the American people will finally prevail," he said.
This article has been updated.