And some Republicans see a political upside in merging negotiations over the funding of the government, with a separate negotiation process over raising the debt ceiling.
If Congress does not vote to raise the debt ceiling by Oct. 17, the country would default on its debts.
President Obama warned Republicans Tuesday against taking this fight to the upcoming debt-ceiling deadline.
"The last time Republicans even threatened this course of action -- many of you remember, back in 2011 -- our economy staggered, our credit rating was downgraded for the first time," Obama said in the Rose Garden Tuesday.
"If they go through with it this time and force the United States to default on its obligations for the first time in history, it would be far more dangerous than a government shutdown, as bad as a shutdown is."
"It would be an economic shutdown."
ABC News' Jeff Zeleny and Alex Lazar contributed to this report.