Speaking with reporters on Capitol Hill, Boehner said House leaders have had "private conversations this week on how we might move ahead but we've not made any decisions at this point."
He said immigration reform presents Congress with "a lot of difficult issues" and members from both sides of the aisle have "done their best" to undermine chances for agreement. When asked to whom he was referring, Boehner said, "You can go find out for yourselves because I think you'll figure it out."
Boehner insisted the House "is going to work its will on immigration."
"We're not going to be stampeded by the White House or stampeded by the president," he said. "The Senate is working its will, a lot of good work that's gone on over there, but the House -- the House will work its will.
"Don't ask me how because if I knew I would certainly tell you, but the House is going to -- the House is going to work its will. And I'm confident that we'll have a solid work product that we can go to conference with the Senate."
Contentious issues include whether a pathway to citizenship would provide healthcare to undocumented immigrants under the Affordable Care Act but House Minority Leader Nancy Pelosi, D-Calif., said the 2010 healthcare reform law already precludes that.
"It is stated very clearly in the Affordable Care Act, [and] it is our position in the immigration bill: no access to subsidies in the Affordable Care Act. Secondly, no access to Medicaid; no cost to the taxpayer," Pelosi said Thursday. "That has always been the Democratic position."
Pelosi said she was concerned about a proposal involving the E-Verify system of determining, for purposes of employment, whether someone is in the country legally.
"They have a trigger in there that says if E-Verify is not fully accomplished in five years ... then all of these people revert to the status that they have now," she said. "I think that's pretty drastic."