Rubio cited growing diversity among Republicans in the Senate as evidence the party had increasing appeal among minorities.
"The Republican Party is the party that placed two Hispanics in the U.S. Senate,” Rubio, a Cuban-American, continued. "And we have an African-American senator in the United States Senate.”
Republican presidential nominee Mitt Romney got trounced by President Obama among Hispanics in the 2012 election. Romney and his GOP challengers tacked to the right on immigration during the campaign, often using harsh terms to frame their conservative positions on the issue.
On Sunday, Powell argued that the GOP has an "identity problem" that puts it out-of-step with the country's changing demographics.
“I think what the Republican Party needs to do now is take a very hard look at itself and understand that the country has changed,” he said. “The country is changing demographically. And if the Republican Party does not change along with that demographic, they're going to be in trouble."
This is not the first time Powell has clashed with his own party. He endorsed Obama in 2008 and again in 2012, but said Sunday he was "still a Republican."