Even as Speaker John A. Boehner pledged to continuing to fight President Barack Obama’s immigration executive orders Thursday, Boehner said he was unclear of Senate Majority Leader Mitch McConnell’s strategy to overcome a Senate Democrat filibuster for a bill funding the Department of Homeland Security and blocking Obama’s actions.

“I’m the Speaker of the House, not of the Senate, so I’m not going to suggest what the Senate should or shouldn’t do,” Boehner said. “All I’ll say is this: The House did its work. We won this fight. … [McConnell has] a tough job over there. I’ve got a tough job over here. God bless him and good luck.”