"Treasury is running out of options and that puts you in a very dangerous position if $10 billion comes in one day and you expected $12 billion," said Steve Bell, senior director at the think tank's Economic Policy Project.
"It would be, in my view, very imprudent ... not to have resolution before then because of the fear of market reaction," he said.
Treasury Secretary Jacob Lew in August told Congress that the United States would need to raise the debt ceiling by the middle of October. Currently, the limit for borrowing is set at $16.7 trillion.
Historically a routine item, Republicans in 2011 decided to hold raising the debt ceiling hostage to demands that the country reduce its debt. The gridlock over the issue prompted credit rating service Standard & Poor's to lower the U.S. credit rating from AAA to AA+, which in turn jolted stock markets.