By Richard Cowan and Yasmeen Abutaleb

WASHINGTON (Reuters) - Senate Republican leaders faced calls from critics within the party on Wednesday for major changes, rather than mere tinkering, to a major healthcare bill if they are to salvage their effort to repeal major parts of the Obamacare law.

In a big setback to the seven-year Republican quest to undo Democratic former President Barack Obama's signature legislative achievement, U.S. Senate Majority Leader Mitch McConnell on Tuesday abandoned plans to get the bill passed this week.

McConnell, with his reputation as a master strategist on the line, put off a vote until after next week's Independence Day recess, when it became apparent he would not muster the 50 votes needed for passage.

Acknowledging demands from fellow Republicans for more input into retooling the legislation, McConnell said on the Senate floor, "Senators will have more opportunities to offer their thoughts as we work toward an agreement."

With Democrats unified against it and Republicans controlling the Senate by a slim 52-48 margin, McConnell can afford to lose only two Republican senators to secure passage, with Vice President Mike Pence able to cast a tie-breaking vote. But at least nine Republican senators - including moderates, hard-line conservatives and others - have expressed opposition to the bill in its current form.

Senate Democratic leader Chuck Schumer challenged Trump to call all 100 senators to the Blair House, across the street from the White House, to craft a bipartisan healthcare bill that would fix, not gut, Obamacare.

"With the demise of this bill yesterday," Schumer said, "we have an opportunity to go back to the drawing board."

The bill drew criticism from Republican moderates worried about millions of people losing their medical insurance and sharp cuts to the Medicaid government healthcare program for the poor, and from conservatives unhappy it did not do enough to erase the 2010 Affordable Care Act, dubbed Obamacare.

"Tinkering will not do it," Republican Senator Bill Cassidy said of efforts to craft a bill that would pass.

"If we do what President Trump suggested, if we put more money back in to try and improve the coverage for those Trump voters who were told on the campaign trail they'd have coverage, their pre-existing (medical) conditions addressed, if we take care of those Trump voters ... then we'll do the right thing," Cassidy told CNN.

The nonpartisan Congressional Budget Office forecast on Monday that the Senate legislation would lead to some 22 million people losing their healthcare insurance over a decade while cutting the federal deficit by $321 billion over that period.

Trump pledged on the campaign trail last year to overturn Obamacare but also promised nobody would lose coverage.

'OVER THE LINE'

"I think we're going to get it over the line," Trump told reporters a day after meeting with most of the Republican senators at the White House to urge them to break the impasse.

Republican Senator Rand Paul, a vocal conservative opponent of McConnell's legislation, said Republican leaders have already done a lot to "placate moderates" and that more elements of Obamacare needed to go to get conservatives on board.

"Obamacare subsidies, keeping Obamacare regulations and creating a new big bailout of insurance companies - conservatives don't like any of those ideas," Paul told MSNBC.

Republicans have called Obamacare a costly government intrusion, and dismantling it became a top priority after they gained control of the White House and both chambers of Congress in January.

The Obamacare law expanded health insurance coverage to some 20 million people, in large part through an expansion of Medicaid.

The Senate legislation would drastically cut Medicaid beginning in 2025, phase out Obamacare's Medicaid expansion, repeal most of the law's taxes, end a penalty on Americans who do not obtain insurance and overhaul Obamacare's subsidies to help people buy insurance with tax credits.

The failure to push the Senate bill through rapidly has exposed frustration among some Republicans over the manner the bill was crafted - by a small group behind closed doors and unveiled only a week ago - and by Trump's changing stances on healthcare legislation.

The House of Representatives passed its version of a healthcare bill last month after a similar struggle to get conservatives and moderates on the same page. The CBO has said some 23 million people would lose their coverage under the House bill over a decade.

Public opinion polls released on Wednesday showed little overall support for the Senate bill.

A Marist/National Public Radio/PBS public opinion poll showed 18 percent of U.S. voters supported it. A separate poll by Morning Consult/Politico, also conducted last week before the CBO issued its analysis, found Republicans evenly split over the Senate proposal's cuts to Medicaid.

Another poll, by Morning Consult/Politico, found that nearly 20 percent of Republicans said the Senate bill went too far in changing the country's healthcare system while 31 percent said it did not go far enough.

(Additional reporting by Susan Heavey, Steve Holland and Mohammad Zargham; Writing by Frances Kerry; Editing by Will Dunham)