The comments seemed a departure from Boehner's recent public comments on immigration, in which he had appeared to be pushing for a deal sometime this year.
His remarks came just two days after Senate Minority Leader Mitch McConnell (R-Ky.) said he thought it would be impossible for the House and Senate to strike a deal that could pass both chambers in 2014. Other Republicans have argued that if Boehner aggressively pursues immigration reform in 2014, it could spell doom for House Republicans who face contentious races in this year's midterms.
The speaker stressed the need for immigration reform, which has been seen as a crucial step as the GOP attempts to strengthen support among Hispanic voters in advance of the 2016 election. But he said a comprehensive reform bill will be "difficult" move through the House and the Senate this year.
"This is an important issue in our country, it's been kicked around forever, and it needs to be dealt with," he said.
But "the American people, including many of my members, don't trust that the reform that we're talking about will be implemented as it was intended to be," he said. "Listen, there's widespread doubt about whether this administration can be trusted to enforce our laws. And it's going to be difficult to move any immigration legislation until that changes."
The speaker also addressed the ongoing debt-ceiling negotiations. He did not rule out the possibility to passing a clean bill but said House Republicans are still considering what, if any, concessions to request from the president in exchange for increasing the nation's borrowing limit.
"We're still looking for the pieces to this puzzle," Boehner said. "We do not want to default on our debt, and we will not default on our debt."
Asked about the reported inability to get House Republicans to buy into plans to demand that the president approve the Keystone XL pipeline project as part of a debt-ceiling deal, Boehner joked:
"Mother Teresa is a saint now, but you know, if the Congress wanted to make her a saint and attach that to the debt ceiling, we probably couldn't get 218 Republican votes."
Boehner's joke about Mother Teresa is not the first acknowledgement by Republicans about the difficulty of lining up their conference behind a debt deal.
On Wednesday, longtime Boehner ally Rep. Patrick J. Tiberi (R-Ohio) said: "Right now, Jesus himself couldn't be the speaker and get 218 Republicans behind something."