Boehner, R-Ohio, said on CBS' "Face the Nation" he was "not going to predict what is going to be on the floor and what isn't going to be on the floor.
"I can't do that, and I don't want to do that," said Boehner.
The speaker said he felt the current U.S. immigration system was "broken" and that "we have got a very big problem." He also said he would stick to his policy of keeping a light hand on the sometimes-restive House in the interest of a fair and open legislative process that would in the long run produce a better immigration bill.
"I've watched a number of speakers during my tenure here in Congress," Boehner said. "I can talk about what happened just before I became speaker. All the bills were written in the speaker's office. Those bills all turned out to be very unpopular."
Notable deaths of 2014 [PHOTOS]