Conservatives said Tuesday there are no plans to attempt to overthrow House Speaker John Boehner, R-Ohio, despite the passage of a $40 billion Homeland Security Funding measure that does not curb President Obama's executive actions on immigration.

Instead, their focus is on Senate Majority Leader Mitch McConnell, R-Ky.

"There is no discussion about deposing the Speaker," Rep. John Fleming, R-La., said. "We elect a new speaker every two years and as far as we are concerned he is going to be our speaker for the rest of this term."

Fleming is a member of the House Freedom Caucus, a faction of about 35 lawmakers who are conservative and tend to buck GOP leaders on legislation they believe veers too far to the middle.

Fleming said the group met this week, and throwing out Boehner is not on the agenda, even though the speaker allowed the Homeland funding bill to pass with mostly Democratic support and the bill does not defund any of Obama's executive actions.

Instead, Fleming said, the Freedom Caucus has set its sights on the Senate. The lawmakers plan to pressure Majority Leader Mitch McConnell, R-Ky., to change the rules of the upper chamber so that legislation can pass with just 51 votes, instead of 60.

"That is the one action that can counterweight a president who acts outside his authority," Fleming said.

Senate Democrats in 2013 changed the Senate rules so that judicial and executive branch appointees required only 51 votes for confirmation. But not even the most conservative GOP senators support altering the rules for passing legislation, which now include a 60-vote threshold in most instances.