If lawmakers do not reach an agreement about the sequester by Oct. 1, the government will shut down and the Treasury will face the risk of default, The Washington Post reported.
The Republican-held House has proposed a bill that would have embraced the sequester while a bill from the Democrat-controlled Senate would have ended it.
"The conundrum is that Republicans know sequestration levels don't work, but they can't figure out how to open the door to solving this problem," Senate Budget Committee Chairman Patty Murray, D-Wash., said. "They have so forcefully fought for the Tea Party agenda, arguing that there is not one good dime spent at the federal level, that they don't know how to get off that and move to compromise."
Meanwhile, President Barack Obama has tried to revive interest in a grand bargain, which would see higher revenues from taxes, sought by Democrats, and cuts to federal health and retirement benefits, which Republicans want.
Obama, as well as White House chief of staff Denis McDonough, has been working with Republican lawmakers to break the deadlock over the budget.
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