Story highlights The House majority leader said the Senate "should waive the 60 rule" on spending bills

Senate Majority Leader Mitch McConnell's spokesman said that change is not in the plans

(CNN) The number two House Republican leader made a fresh push Wednesday for Senate Republicans to change rules to make it easier to break filibusters of spending bills, echoing a similar call from President Donald Trump for the Senate to set aside long-held precedent that requires at least 60 votes for major legislation to pass.

Majority Leader Kevin McCarthy boasted that the House was on the verge of passing all 12 annual appropriations measures, something that hasn't happened since 2004.

"We will pass them with a majority in Congress. I believe the Senate should do the same, with a simple majority of the Senate," McCarthy told reporters. "The Senate should waive the 60 rule and pass it with a simple majority and take it to the President's desk."

But McCarthy's proposal, which he called for also in 2015, was immediately rejected by the top GOP leaders in both the Senate and the House.

Senate Majority Leader Mitch McConnell's spokesman Don Stewart told CNN, "The Senate Republican conference does not support changing the threshold for cloture motions on legislation."