The Ohio Republican dodged seven direct questions Sunday on the CBS News program "Face the Nation" about whether immigration reform should include path to citizenship for the 11 million immigrants living in the United States illegally -- a provision opposed by many conservative Republicans.
The Senate passed a bipartisan bill June 27 that includes this provision, with a 13-year path to citizenship.
Boehner has said the House would not consider the Senate bill, which he has called "flawed legislation rushed through the Senate." He said the lower chamber would instead consider immigration in smaller, "bite-sized" pieces over the coming months.
The proposed House DREAM Act substitute bill, likely to be called the KIDS Act, would offer a path to citizenship for young people brought by their parents to the country illegally as minors, but exclude their parents from the possibility of citizenship.
On "Face the Nation," Boehner first answered the question about a citizenship pathway by saying the immigration system was broken. He said the Senate bill, which passed 68-32, didn't have "enough serious triggers to protect our borders."
Asked a second time, he said the House would deal with immigration "in a common-sense, step-by-step approach."
"We want to deal with this in chunks -- chunks that the members can deal with and grapple with and frankly chunks that the American people can get their arms around," he said.
When asked if he was not going to answer the question, Boehner said: "It's not about me. This is about allowing the House to work its will."
He was asked if he would even allow a bill to be introduced if it includes a path to citizenship.
"I'm not going to predict what's going to be on the floor and what isn't going to be on the floor," Boehner said. "Now that's what you're asking me to do. I can't do that, and I don't want to do that."
Boehner -- whose district is 90.4 percent white and 1.3 percent Hispanic -- also wouldn't say if he himself favored a bill that has a path to citizenship and wouldn't say if the Republican Party could survive without passing immigration reform that includes a path to citizenship.
Many GOP leaders have said this issue, which has become central to the debate on overhauling the immigration system, is vital to the party's ability to remain relevant among voters, including the growing Latino electorate.
But many House Republicans have few minority voters in their districts and see the issue as a low priority, the Los Angeles Times said.
"This isn't about politics and it's not about our party. This is about doing the right thing for our country. We're a nation of immigrants. Immigration has strengthened our country. We have got a broken system. My job is to work with the House members on both sides of the aisle, facilitate a conversation and facilitate a process where we can deal with this honestly and openly," Boehner said.
He denied he was refusing to take a stand because he has struggled to lead his often unruly majority.
A House Judiciary Committee panel plans Tuesday to hold a hearing on the KIDS Act, crafted by Majority Leader Eric Cantor, R-Va., and Judiciary Committee Chairman Bob Goodlatte, R-Va.
"These children came here through no fault of their own and many of them know no other home than the United States," Goodlatte said in a statement Thursday.
"This is one component of immigration reform -- any successful reform plan must improve our legal immigration programs, strengthen border security and the interior enforcement of our immigration laws, and find a way to fairly deal with those who are currently in the country unlawfully," Goodlatte's statement said.
The DREAM Act -- which would grant an expedited path to citizenship to people brought to the United States illegally as children if they meet certain conditions, such as attending college or serving in the military -- was included in the Senate's immigration reform bill.
Senate Majority Leader Harry Reid, D-Nev., has said the KIDS Act would be dead on arrival in his chamber.