Tourists walk past US Park Service rangers manning a barrier at the World War II Memorial in Washington, as the partial government shutdown entered day six on Sunday. Mike Theiler / Reuters

As the US government moved into the second week of a shutdown on Monday with no end in sight, a deadlocked US Congress also confronted an Oct 17 deadline to increase the nation's borrowing power or risk default.

The last big confrontation over the debt ceiling, in August 2011, ended with an eleventh-hour agreement under pressure from shaken markets and warnings of an economic catastrophe if a default were allowed to occur.

A similar last-minute resolution remained a distinct possibility this time as well.

In comments on Sunday political talk shows, neither Republicans nor Democrats offered any sign of impending agreement on either the shutdown or the debt ceiling, and both blamed the other side for the impasse.

"I'm willing to sit down and have a conversation with the president," said Republican House of Representatives Speaker John Boehner, speaking on ABC's This Week. But, he added, US President Barack Obama's "refusal to negotiate is putting our country at risk".

On CNN's State of the Union, US Treasury Secretary Jack Lew said: "Congress is playing with fire," adding that Obama will not negotiate until "Congress does its job" by reopening the government and raising the debt ceiling.

The shutdown has pushed hundreds of thousands of workers off the job, closed national parks and museums and stopped an array of government services.

The one bright spot on Monday is a significant chunk of the furloughed federal workforce is headed back to work. US Defense Secretary Chuck Hagel ordered nearly 350,000 back on the job, basing his decision on a Pentagon interpretation of a law called the Pay Our Military Act.