Speaker of the House John Boehner on Tuesday said the government shutdown could last a week or longer but that near-term budget talks toward a resolution are possible, a top aide to the Republican leader told CNBC.
The same aide had previously said any shutdown would be short-lived.
President Barack Obama has said he is open to budget talks, as opposed to the debt limit, on which he has indicated there is no room for negotiation.
(Read more: Obama: GOP shut down government over 'ideological crusade')
The aide suggested Republicans may be willing to trade some sequester cuts, which are unpopular with both parties, in exchange for cuts in entitlements, which Democrats hope to protect.
Budget talks such as these may come easier than those targeting the president's signature legislation, the Patient Protection and Affordable care Act, the aide said.
Meanwhile, House Republicans aim to re-start some functions of the federal government, bringing up bills to fund the National Park Service, part of the Department of Veterans Affairs and capital city operations, in a gambit to deflect blame for the shutdown, The Hill reported.
The House is expected to vote early Tuesday evening on three separate bills. Because they would require a two-thirds majority to pass, the measures would need significant Democratic support and would allow Republicans to blame Democrats if they failed.
Earlier in the day, a group of U.S. war veterans forced their way past barriers to visit the U.S. Veterans Memorial in Washington D.C. It had been closed to visitors because of the shutdown.
(Read more: WWII vets are crashing the WWII Memorial: Reporter)