President Barack Obama has so far refused to negotiate with Republicans who are insisting that any government funding bill must somehow delay, defund or otherwise disrupt his showpiece healthcare programme dubbed 'Obamacare'.
Obama said he will not bow to Republicans' demands that he enter negotiations with them even risking a continued shutdown or the first-ever debt default in US history.
Republicans remain undeterred, saying they would neither raise the USD 16.7 trillion debt ceiling nor reopen the government without first winning concessions.
Democrats say they may also accept a short-term bill, perhaps lasting only weeks, if necessary to avoid going over the brink.
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The Democratic push on the debt limit came as the shutdown entered its eighth day with no solution in sight.
The White House has already warned that the looming prospect of a debt default by the world's largest economy was a "terrible" scenario that would harm America's democracy and global stature.
The shutdown has left federal employees on unpaid leave and closed national parks, tourist sites, official websites, office buildings, and more establishments since last Tuesday.
Congress must act by October 17 in order to avoid a debt default by the US government which will run out of cash on that day for the first time in US history unless its debt ceiling is raised.