Meanwhile, Vice President Joe Biden is leading a series of meetings with Republican and Democratic leaders, and administration officials to hash out a deal.
After their third round of talks, Biden Thursday said the group is "actually making progress" but "nothing is agreed to until everything is agreed to."
Republicans echoed that sentiment but they are unwilling to budge from their original demands of taking a scalpel to spending.
"We have a $14 trillion debt in this country," Sen. John Barasso, R-Wyo., said in an interview with Fox on Thursday. "The president wants to raise the debt ceiling. I am not ready to give him a blank check or a new credit card. We did talk about the need to put a cap on spending, as opposed to a total debt cap, which the president, I think, is more interested in having, which would involve additional taxes. ... But raising the tax rates, to me, is completely off the table."
Others, such as Senate Minority Leader Mitch McConnell on Kentucky, argue that any budget talks have to include a discussion of Medicare and Medicaid overhaul.
The next set of meetings is scheduled for after Memorial Day weekend.
Meanwhile, Tea Party leaders are warning that they are keeping a close eye on Congress members' voting records, for the next election.
"We are tired of the lip service. We want to see action follow through on your campaign promises," Kremer warned lawmakers. "[Otherwise] you will be fired just as fast as you were hired."