The Democratic Congressional Campaign Committee has also been raising money off a potential shutdown this week.
"Contribute $3 or more to the GOP Accountability Fund right now to help us raise $50,000 in grassroots contributions by Friday's deadline so we can hold Speaker Boehner and his Tea Party fringe Republicans immediately accountable for shutting down the government," DCCC Chair Steve Israel wrote in a fundraising email Wednesday.
Republicans pounced on the DCCC fundraising pitch.
"House Democrats are exploiting our financial crisis and using it for political gain while Republicans are addressing it as an American challenge that calls for placing our nation and our economy ahead of partisanship," said National Republican Congressional Committee spokesperson Joanna Burgos.
--Jessica Taylor contributed to this report.