Some Republicans have warned that they may use impending negotiations about the US debt ceiling to exact greater demands on a range of policies from President Barack Obama.
House Republicans have sought concessions and delays to the healthcare bill known as Obamacare, but these have been rejected by the Democrat-controlled Senate.
Representative John Fleming warned there "will be an even bigger list when it comes to the debt ceiling," which must be agreed by 17 October.
"We're going to be talking about the Keystone XL pipeline, movement of cuts into entitlement reforms, beginning to adjust sequester," he said.
The US shutdown is but a precursor to a much bigger problem - in a couple of weeks the government, shutdown or not, will run out of cash.
Landmarks across the US have closed as the Congress failed to reach a deal over the budget.