The US Senate has voted to approve a $1.9 trillion relief package in what President Joe Biden called a "giant step" towards reviving the pandemic-stricken American economy, capping frenzied negotiations and a marathon overnight voting session.

Passed by 50 votes to 49 in a strict party-line vote, the sweeping legislation now heads back to the Democratic-majority House of Representatives, where it is expected to be adopted, barring a last-minute setback.

"I promised the American people help was on the way," said Biden in an address from the White House, after the plan was approved along strict party lines.

"Today, I can say we've taken one more giant step forward in delivering on that promise," he said. "It obviously wasn't easy. It wasn't always pretty. But it was so desperately needed."

Even without the progressive priority of a minimum wage increase to $15 an hour, the stimulus bill marks a victory for Biden's Democrats as they put their stamp on the recovery from a pandemic that has killed more than 500,000 people in the United States and hobbled its economy.

Top Senate Democrat Chuck Schumer vowed that the bill "will deliver more help to more people than anything the federal government has done in decades." 

The legislation would send out $1,400 stimulus checks to most Americans and allocates $350 billion to state and local governments and $130 billion to schools.

It would also provide $49 billion for expanded Covid testing, tracing and research, and $14 billion for vaccine distribution.

Steny Hoyer, the Democratic majority leader in the House, said the chamber would take up the amended bill on Tuesday, with a view to sending it to Biden for his signature early next week.

- Vote-a-rama -

The huge bill -- the second largest rescue package in US history, after last year's $2 trillion CARES Act -- almost fell apart. 

Senate action was paralyzed for more than 10 hours Friday as Democrats scrambled to retain the support of their most conservative senator, Joe Manchin, who balked at the scale of jobless benefits.

It took a call from Biden and a cut in supplemental weekly unemployment insurance from $400 to $300, among other tweaks, to prevent Manchin from defecting.

The drama served to highlight the growing political muscle of moderates in a deadlocked Senate, where a single swing vote could make or break major legislation.

Biden already had to compromise with Democrats urging more fiscal restraint, reportedly agreeing to a narrowing of the income limit for families receiving stimulus checks.

But the president struck an upbeat note, insisting: "I don't think any of the compromises have in any way fundamentally altered the essence of what I put in the bill in the first place."

"This plan is historic," Biden said. "This plan will get checks out the door starting this month to the American people who so desperately need the help," he said, "many of whom are lying in bed at night, staring at the ceiling, wondering, will I lose my job...? Will I lose my insurance? Will I lose my home?"

The breakthrough on the bill came on Saturday against a backdrop of strong US economic data signaling that the world's largest economy may finally be healing, including better-than-expected hiring in February as battered businesses began recruiting again.

Yet the economy was still short 9.5 million jobs compared with February 2020.

Treasury Secretary Janet Yellen welcomed the Senate vote, saying that without it, it might take two years for the economy to return to pre-Covid levels, creating "economic scars that last well beyond the end of the pandemic."

- 'Wish-list' -

Over a rapid-fire but lengthy series known as a "vote-a-rama", bleary-eyed senators acted on dozen of amendments, mostly Republican proposals that failed but which forced rival Democrats into casting politically fraught votes.

Republicans have been united in opposition to the bill, and Senate Minority Leader Mitch McConnell issued a statement slamming a "colossal missed opportunity for our nation."

"Democrats decided their top priority wasn't pandemic relief, it was their Washington wish-list," he charged.

Although Biden had promised during the 2020 election campaign to work as much as possible with Republicans, he was unable to attract even a single vote from the opposition party.

But he dismissed the notion that was a bad omen for bipartisanship going forward.

"Look, the American people strongly support what we're doing," Biden told reporters. "That's the key here. And that's going to continue to seep down through the public, including from our Republican friends."