But neither party sees a government shutdown as a solution to the United States' growing deficit, The Hill reported.
"One thing we can't do is take extreme steps like shutting down the government and forcing the United States government to default on its obligations," said Senate Majority Leader Harry Reid, D-Nev.
If there is a shutdown, it will be because of Republicans, said Sen. Chuck Schumer, D-N.Y.
"Too many Republicans seem to want to force a government shutdown," Schumer said. "That would be the same mistake they made in 1995. It would be an even bigger mistake now. It's playing with fire."
The government briefly shut down in 1995 following a budget stalemate between President Clinton and Republicans led by House Speaker Newt Gingrich.
Republicans contend Democrats are talking about a shutdown to boost their image.
"As Republicans focus on constructive ways for the two parties to work together on cutting spending and debt, Senator Schumer seems strangely preoccupied with the notion of a government shutdown," said Don Stewart, a spokesman for Senate Republican Leader Mitch McConnell.
"It is our hope that he soon realizes the only person talking about a shutdown is Senator Schumer," Stewart said.