But perhaps expressing the sentiments of many of his colleagues, Reid suggested he would not mind holding the vote earlier, during the work week, if Republicans would agree to abbreviate the percolating period demanded by Senate rules. 

"If the proponents of the bill decide they would like to vote sooner, let me know, I would appreciate that," Reid said. "We will try to work something out."

Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenate tees up Yemen vote for Tuesday Senate confirms Trump's border chief House leaves out ObamaCare fix from must-pass funding bill MORE (R-Ky.), however, kept his cards close to his chest, and gave no indication his caucus would be willing to budge. 

"I share the view of the majority leader," said Reid. "We should have a vigorous debate over ‘cut, cap and balance,’ and I look forward to being here Saturday to vote to proceed to that bill."

The "cut, cap and balance" bill passed the House Tuesday evening in a 234-190 vote, but the legislation is expected to fall short in the Senate. 

President Obama has also threatened to veto it.

The legislation would cut spending by $111 billion in 2012, cap spending over the next decade and prohibit more borrowing until Congress passes a balanced-budget amendment to the Constitution.