The US government is on the precipice of a historic shutdown that would result in hundreds of thousands of federal workers being placed on unpaid leave, after House Republicans refused to pass a budget unless it involved a delay to Barack Obama's signature healthcare reforms.

Democratic leaders declined to convene the Senate on Sunday, standing firm against what they described as the extortion tactics of their Republican opponents who they accused of holding the government to ransom for ideological reasons.

The resolution passed by the Republican-controlled House of Representatives in the early hours of Sunday morning makes funding the government until the middle of December contingent upon a one-year delay of the Affordable Care Act. It also strips the new healthcare law, which is due to come into force on Tuesday, of a key tax on medical devices.

Senate Democrats and the White House have said they will block any budget resolution that is tied to the healthcare law – known as Obamacare – which was passed three years ago and upheld by the US supreme court last year.

Undermining the healthcare reforms – the flagship legislative achievement of Obama's presidency – has been a priority for the conservative wing of the Republican party for years and the spectre of government shutdowns has been used in the past.

However there was a growing sense on Capitol Hill on Sunday that House Republicans were prepared to see through their threat of a shutdown, which would begin at 12.01am ET on Tuesday, even though polls show they would be blamed for a maneuver that could damage the party during next year's midterm elections.

"Republicans in Congress had the opportunity to pass a routine, simple continuing resolution that keeps the government running for a few more weeks," said White House spokesman Jay Carney. "But instead, Republicans decided they would rather make an ideological point by demanding the sabotage of the healthcare law."

Harry Reid, the Senate leader who on Saturday said he would refuse to bow to "Tea Party anarchists", showed no interest in negotiating with Republicans over the stalemate. He was criticised by leading Republicans for failing to invite the Senate to debate the House resolution, less than 36 hours from the budget deadline.

Instead, the Senate was expected to wait until Monday before stripping the Republican motion of its references to Obamacare and, for the second time in a week, returning a "clean" bill to the House that would fund federal departments, without also impeding the introduction of mandatory healthcare for Americans who are uninsured.

If there is time, the House would then have just a few hours to either vote to fund the government, free of any measures that would impede the introduction Obamacare, or trigger the first American government shutdown in 17 years.

Asked if he thought a shutdown was now inevitable, Richard Durbin, the second most senior Democrat in the Senate, replied: "I'm afraid I do."

Durbin told CBS's Face the Nation that he was open to negotiating over the tax on medical devices, "but not with a gun to my head, not with the prospect of shutting down the government".

Senior Republicans took to the Sunday morning talk shows to defend their stance, claiming that it was Democrats who were forcing a shutdown by refusing to compromise over the controversial healthcare reforms.

Congresswoman Cathy McManus Rogers, chair of the House Republican conference, said Reid was acting irresponsibly by refusing to hold a session of the Senate. "They're the ones threatening a government shutdown by not being here," she said.

Ted Cruz, the Republican senator spearheading the congressional campaign to undo Obama's healthcare reforms, turned the debate on its head by accusing Democrats of holding "political brute force" for refusing to delay or unravel the healthcare law.

"If we have a shutdown, it will be because Harry Reid holds that absolutist position and essentially holds the American people hostage," Cruz, who this week gave a 21-hour speech to draw attention to his campaign, said on NBC's Meet the Press.

"So far, majority leader Harry Reid has essentially told the House of Representatives and the American people, 'go jump in a lake'," Cruz added. "He says: 'I'm not willing to compromise, I'm not willing to even talk.' His position is, 100% of Obamacare must be funded in all instances. Other than that, he's going to shut the government down."

The impact of any federal shutdown would depend upon how long it lasts. Under contingency arrangements, essential services such as law enforcement, will be kept alive, although hundreds of thousands of federal workers would be placed on unpaid leave.

Social security and Medicare benefits would continue, and air traffic controllers would remain in place to ensure airports function. However museums, national parks and landmarks such as the Statue of Liberty and Washington Monument, would be closed.

The military's 1.4 million personnel active duty would remain in post, but their paychecks would be delayed. About half of the Defense Department's civilian employees – about 800,000 people – would be furloughed, meaning they would be suspended from work without pay.

Federal courts would continue to function as usual for around a fortnight, after which the judiciary would have to start shelving work that is not considered essential.

The gridlock over the government budget could be just the prelude to an even more serious showdown expected in mid-October over the government debt ceiling.

Republicans are threatening to refuse to lift the ceiling unless Obamacare is reined back, which could mean the US Treasury would be forced to default on its debt payments.