Speaker John Boehner (R., Ohio) and House Minority Leader Nancy Pelosi (D., Calif.) didn’t cut a deal so much as come to an “understanding” about how the debate over the Department of Homeland Security funding bill would wind down.
“[Pelosi] had an idea. According to a source with knowledge of the conversation, the minority leader started the call with these words: ‘Here’s what I’m thinking in interest of saving face,’” she said, per Roll Call. “Pelosi and Boehner discussed a number of options, but settled on ‘an understanding.’ Democrats could utilize Rule XXII to bring up the Senate bill this week, as long as Pelosi agreed to get her party to pass a one-week continuing resolution for DHS.”
In a sense, Boehner didn’t have to give up much, because the rules were already in place: if the Senate Democrats blocked a vote on creating a conference committee that could resolve the differences between the House-passed and Senate-passed DHS funding bills, then any House member could bring the Senate bill to the floor, unless the House voted to change the rules. In this case, Republicans either had the votes to block the DHS bill or not; if they didn’t, they probably wouldn’t have the votes to change the rules to stop the bill from getting a vote.
In the event, Boehner told the GOP conference that Democrats had this power, but he called for a Republican to call it up rather than a Democrat, and that’s what happened.