Not passing immigration reform would be "damaging to the country," said U.S. Sen. John McCain, in urging the U.S. House of Representatives to pass a measure the Senate already approved.

Republican House Speaker John Boehner has said immigration and border security reform measures are unlikely to get a vote in the House, but McCain is still pushing for action, even if the bills are considered in a piecemeal process, as opposed to one comprehensive bill.

"I remain hopeful because the prospect of not passing immigration is damaging to the country and to the Republican Party, in that order," he said.

Republicans are essentially doing something they've said they are against, he said, if they don't pass changes.

"There are 11 million people who are in this country illegally. They're not going to be deported. And so to not enact comprehensive immigration reform, that's de facto amnesty," McCain said.

McCain said human rights abuses and other problems are exacerbated because of undocumented immigration and the Congressional Budget Office estimates reform would bring in more revenue for the Social Security system and increase the country's gross domestic product.

"I feel very strongly that we need to act and unleash the strength and entrepreneurship and contributions that people who are in this country as immigrants can provide," he said.