Conservatives, including members of the Senate Tea Party Caucus, are also unhappy with the proposal.

McConnell's plan would require Obama to make three separate requests to raise the debt limit. Congress could pass resolutions of disapproval to block the requests, but those actions would require two-thirds' support in both chambers in order to override expected presidential vetoes.

The proposal from the Senate Republican leader would require Obama to request three tranches ranging between $700 billion and $900 billion. Those requests would be made at the end of this month, later this fall and in the summer of 2012.

It also would require Obama to recommend a greater amount of spending cuts for every dollar he requests to raise the debt limit.

Senate Majority Leader Harry ReidHarry ReidTrump flirts with Dems for Cabinet Lawmakers eye early exit from Washington McCain to support waiver for Mattis, Trump team says MORE (D-Nev.) earlier in the week said he was “heartened” by the plan, and Majority Whip Dick DurbinDick DurbinLawmakers eye early exit from Washington Senators crafting bill to limit deportations under Trump Warren pushes Dems to get tough with Trump MORE (D-Ill.) also offered praise, calling it a "positive and thoughtful response" to the need to raise the debt ceiling.