Two leading GOP voices on immigration reform on Wednesday said that the Republican Party has to accept immigration reform or die at the ballot box.

In different tones, Arizona Sen. Jeff Flake, a member of the Senate Gang of Eight working on the issue, and Sen. Rand Paul, a likely Republican 2016 presidential candidate, said the GOP has little choice but to approve reform that includes legalizing the 11 million undocumented workers in America.

"I've believed for a long time that this issue makes it very difficult for Republicans to compete nationwide and state by state. I do," said Flake. "Going forward it behooves us as Republicans to solve this issue."

Flake said that winning Hispanics, the fast-growing minority in the nation, comes down to showing them that Republicans care. "It's tough to compete for their votes or enter a discussion if they think you don't like them and I think that most Republicans have to conceded after the last election that that was the view of many groups," Flake said at a newsmaker breakfast hosted by the Christian Science Monitor.

"Politically," he added, "it would help us."

In a separate appearance, Paul urged both sides to embrace immigration reform. Part of Paul's message was targeted to Republicans. "The Republican Party must embrace more legal immigration," he said.

Flake said that there is a possibility that many Republicans could vote for the immigration bill now before the Senate, especially if border security is tightened. "It's possible to hit the 70 [vote] mark that's been talked about or maybe beyond," he cheered at the breakfast where he sat with fellow Gang of Eight member Sen. Michael Bennet of Colorado.

Bennet and Flake said that the bipartisan immigration bill, if passed, could become the model for future legislative deal-making and Flake even gave an example of how close he's become to Democrats while working the issue.

"I share Michael's hope that this leads to other areas of cooperation," said Flake, who added: "I was back in the House gym the other day with some old colleagues and they said, 'Who are you spending time with in the Senate now?' They thought I'd say [conservative Sens.] Pat Toomey or Tim Scott. I said, [liberal Sens.] 'Chuck Schumer, Dick Durbin, Michael Bennet.' It's not what I expected, but it's been a great process and I hope it continues and spreads to other areas particularly on the budget."