(Adds Sanders statement, comment by Tester on meeting with Biden)

By Susan Cornwell and David Morgan

WASHINGTON, March 1 (Reuters) - The U.S. Senate will start debating President Joe Biden's $1.9 trillion coronavirus relief bill this week, Senate Majority Leader Chuck Schumer said on Monday after Democrats backed down from an effort to raise the minimum wage to $15 as part of it.

The backpedaling did not end hopes of addressing the minimum wage issue in Congress. Democrats and some Republicans have voiced support for the idea of raising the federal minimum wage, now at $7.25 an hour, for the first time since 2009, although they disagree on how much.

Republican Senators Mitt Romney and Tom Cotton last week proposed an increase to $10 per hour, but said employers should verify the wage is going to workers who are legally in the United States.

The Democratic-controlled House of Representatives early on Saturday narrowly approved the COVID-19 package, one of Biden's top priorities. The House bill included the minimum wage hike.

Democrats aim to pass the legislation in the Senate trough a maneuver known as "reconciliation," which would allow the bill to pass with a simple majority rather than the 60 votes normally required by that chamber's rules.

Senate debate on the COVID-19 bill could begin as early as Wednesday, a Senate Democratic aide said.

Senate Democrats over the weekend gave up on the idea of trying to pass the minimum wage hike by adding tax penalties to the COVID-19 bill, after earlier being told that Senate rules governing "reconciliation" prevented them including a straight-up wage hike to the legislation.

There are also political hurdles. Some moderate Democrats, including Senator Joe Manchin, have rejected the $15 figure as too high and suggested an $11 target could be more realistic.

"We worked through the weekend and it became clear that finalizing 'plan B' with the caucus would delay passage and risk going over the jobless benefits cliff on March 14," one source said. Democrats want the COVID-19 bill signed into law by March 14, when enhanced unemployment benefits expire.

A group of House progressives urged Biden on Monday to overrule the Senate parliamentarian, who determined last week that the $15 proposal could not pass by reconciliation.

"This ruling is a bridge too far," said Democratic Representative Ro Khanna. "If we don’t overrule the Senate parliamentarian, we are condoning poverty wages for millions of Americans."

The White House has previously ruled out intervening.

Senator Bernie Sanders, an independent who caucuses with the Democrats, said on Monday night he would introduce an amendment to increase the federal minimum wage to $15 an hour by 2025 in the final reconciliation bill, adding he believed the Senate should ignore the parliamentarian's advice.

"I am not sure, however, that my view at this point is the majority view in the Democratic Caucus," Sanders said in a statement.

The Senate's No. 2 Democrat, Dick Durbin, told reporters that lawmakers should look for another venue to raise the minimum wage, but that "if it takes some 60 votes or a supermajority of some kind, it's going to be very difficult, obviously."

REPUBLICANS BLAST PLAN

To pass the relief plan, Democratic Vice President Kamala Harris may have to cast a tie-breaking vote in a chamber where Republicans control 50 seats and Democrats and their allies control the other 50. Even that outcome depends on all the Democrats staying united behind the first major bill to come through Congress in the Biden administration.

Democrats say the package is needed to fight a pandemic that has killed more than 500,000 Americans and thrown millions out of work.

Biden met with nine Senate Democrats on the coronavirus relief bill on Monday. One of them, Senator Jon Tester, told reporters they discussed "targeting" the funds in the legislation.

"At least from my perspective, it wasn't talking about reducing it, just targeting the money," said Tester.

Republicans in Congress, who broadly backed COVID-19 relief spending early in the pandemic, say the relief plan is too expensive and includes things like transportation projects that have nothing to do with relief for COVID-19. They also do not like the $35 billion included for pumping up government subsidies to defray the cost of premiums in the Obamacare health insurance program.

Senate Minority Leader Mitch McConnell denounced the measure on Monday as a "bonanza of partisan spending" that poorly targets the needs of American families, devotes only 1% of its spending to vaccines, delays the bulk of its school aid until after 2021 and includes policies that would drag down the economy.

"This is where we are: a bad process, a bad bill, and a missed opportunity to do right by working families," McConnell said in a Senate floor speech.

The Democratic measure includes funding to track the virus and distribute vaccines, and sends a new round of aid to households, small businesses and state and local governments.

The big-ticket items include $1,400 direct payments to individuals, a $400-per-week federal unemployment benefit through Aug. 29 and help for those in difficulty paying rents and home mortgages during the pandemic.

(Reporting by Susan Cornwell and David Morgan; Additional reporting by Makini Brice; Editing by Scott Malone, Alistair Bell and Peter Cooney)