"Should I win a second term, a big reason I will win a second term is because the Republican nominee and the Republican Party have so alienated the fastest-growing demographic group in the country, the Latino community," Obama said. "And this is a relatively new phenomenon. George Bush and Karl Rove were smart enough to understand the changing nature of America. And so I am fairly confident that they’re going to have a deep interest in getting that done. And I want to get it done because it’s the right thing to do and I've cared about this ever since I ran back in 2008."

Bush was able to reverse dwindling support for Republicans among Latinos in both of his successful presidential campaigns. After 25 percent of Latinos voted for the Republican candidate in 1992 and 21 percent in 1996, 35 percent voted for Bush in his first successful presidential campaign in 2000 and 44 percent voted for him again in 2004.

Recently, Rove warned that the Republican party would be doomed without the support of the Latino population.

"If we do with Latinos what we did with African-Americans, Republicans and conservatives will be doomed,” Rove said Thursday, according to the Associated Press.

In response, Rove released a statement later on Wednesday saying Obama should have introduced comprehensive immigration reform when Democrats controlled both the Senate and the House in the first two years of his presidency.

"I appreciate President Barack ObamaBarack Hussein ObamaTrump's tariffs are a case of crony capitalism Obama to visit Kenya, South Africa for Obama Foundation in July Overnight Energy: EPA declines to write new rule for toxic spills | Senate blocks move to stop Obama water rule | EPA bought 'tactical' pants and polos MORE's comments to the Des Moines Register crediting President George W. Bush for advocating comprehensive immigration reform, but I would have rather seen his support for the Comprehensive Immigration Reform Act of 2007 when he was the junior Senator from Illinois, or his introducing an immigration bill when he enjoyed Democratic majorities in both the House of Representatives and the Senate during his first two years as president," Rove said in the statement.

Rove went on to say that it is unlikely that Obama would have a chance to pass immigration reform in a second time.

"He says he's "fairly confident" Republicans will have a "deep interest" in getting immigration reform done in his (unlikely) second term, but his record does not convince me he would be as committed," Rove said. 

—This story was updated at 4:18 p.m.