Democrats and a number Republicans are calling for a bipartisan effort to improve the US’s healthcare system after the Senate’s Republican leadership suffered a colossal defeat in their attempts to overhaul Obamacare.

A promise to repeal and replace the healthcare legislation, which was a pillar of former Democratic President Barack Obama’s legacy, was central to Donald Trump's presidential campaign. And Mr Trump was quick to express his dismay at the failure of the bill, which still leaves him without a significant legislative win.

Addressing police officers in Brentwood, New York, Mr Trump said: “I said from the beginning, let Obamacare implode and then do it [pass legislation]. I turned out to be right. Let Obamacare implode.”

Mr Trump, who earlier on Twitter said the three Republicans who voted no “let America down,” again took aim at those in his own party who failed him. “Boy, oh boy, they've been working on that one for seven years,” he said. “Can you believe that? The swamp. But we'll get it done.”

In the early hours of Friday morning, the Senate voted 49-51 against legislation that would have rolled back provisions of the Affordable Care Act, otherwise known as Obamacare. The law, passed in 2010, has provided millions of people with health insurance coverage. But Republicans say it has driven up premiums and forced consumers to buy insurance they do not want and cannot afford.

“Obamacare was hardly perfect,” said Senate Minority Leader Charles Schumer following the failed repeal vote. “It did a lot of good things, but it needs improvement. And I hope one part of turning page is that we go back to regular order, work in the committees together to improve Obamacare.”

“I hope this is a turning point,” he added.

Senate Majority Leader Mitch McConnell has invited Democrats to share their ideas on how to better the US healthcare system, but expressed scepticism about whether they would provide any useful suggestions. He said he doubted any Republicans would support “bailing out insurance companies with no thought of any kind of reform”.

“It’s time for our friends on the other side to tell us what they have in mind, and we’ll see how the American people feel about their ideas,” Mr McConnell said on the Senate floor.

During a news conference on Friday, Mr Schumer asserted that there could be bipartisan support for some ideas to help stabilise the individual insurance markets created by Obamacare.

The Democratic leader suggested that Congress should provide money for subsidy payments – known as cost-sharing reduction payments – to health insurance companies, which have been demanding big rate increases or fleeing from Obamacare markets. Making the payments could be key to keeping insurers in the market and preventing spikes in premiums.

While the Trump administration has threatened to cancel those payments to destabilise markets and bring Democrats to the negotiating table on healthcare reform, some powerful Republican legislators have also called for guaranteeing the cost-sharing subsidies.

“I hope we can work together in a bipartisan way, and I’m optimistic that that can happen,” Mr Schumer said.

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House Minority Leader Nancy Pelosi urged Republicans to establish a process to move forward on improvements to Obamacare.

“We call upon the speaker to establish a process – we can go right to the committees – and have the discussion on how we keep America healthy,” Ms Pelosi said.

Republican senators John McCain and Susan Collins, both of whom voted to block their party's latest Obamacare repeal plan, have also called for a bipartisan fix for insurance markets.

In a statement explaining why he voted ‘no’ on Friday morning, Mr McCain said he did not believe in forcing through changes to the healthcare law without at least some support from Democrats.

“I’ve stated time and time again that one of the major failures of Obamacare was that it was rammed through Congress by Democrats on a strict party-line basis without a single Republican vote,” he said. “We should not make the mistakes of the past.”

But while some senators from both parties appear ready to write a healthcare bill on a bipartisan basis, House Speaker Paul Ryan has said that Republicans “should not give up” after promising for seven years to repeal and replace Obamacare.

“We were sent to Washington to fulfill the pledges we made to our constituents,” Mr Ryan said in a statement. “While the House delivered a bill to repeal and replace Obamacare, unfortunately the Senate was unable to reach a consensus.”

Both Mr McConnell and Mr Ryan have said their respective chambers of Congress will move on from healthcare to different matters for the time being, and it is unclear whether Republican leaders will resuscitate efforts to repeal and replace the ACA.

Meanwhile, Republican congressman Steve King lashed out against Republicans in the Senate who helped defeat the party’s legislation, saying in a statement that the ACA is a “law that ought not exist, and I will continue to advocate for its complete repeal.”

Mr King singled out senators Lisa Murkowski and John McCain, who has diagnosed with brain cancer earlier this week and returned to Washington for the healthcare debate.