* McConnell meets Republican senators, seeking path forward
* Key senator says goal is to work out changes by Friday (Adds comments by Trump, Sanders, Collins, background on Democrats and Obamacare)
WASHINGTON, June 28 (Reuters) - Senate Republican leaders faced calls from critics within the party on Wednesday for substantial 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, after 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."
McConnell met with a procession of Republican senators in his office, including some who have criticized the bill. John Cornyn, the No. 2 Senate Republican, said the party leadership would be talking to every Republican senator who had expressed concerns or was undecided about the bill.
Cornyn told reporters it would be "optimal" to have changes to the legislation worked out by Friday so that a new version could be analyzed by the nonpartisan Congressional Budget Office. The CBO forecast on Monday that the existing bill 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.
The prospect of so many people losing insurance is unpalatable to moderates such as Senator Susan Collins, a key opponent of the draft legislation. Collins said it would be "very difficult" to reach agreement on the bill by Friday.
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. 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 President Donald 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."
Trump told reporters he did not think Schumer was serious in his offer. White House spokeswoman Sarah Sanders was also dismissive, saying Democrats "have frankly refused to be a part of the conversation from the beginning."
The 2010 Affordable Care Act, dubbed Obamacare, passed with no Republican support and has long been a strong marker of partisan divide in Congress. While Schumer and other Democrats have repeatedly said talking about a repeal of Obamacare is a non-starter, they have said they would be willing to talk about ways it could be improved.
The Senate bill drew criticism from Republican moderates worried about rising numbers of uninsured people and sharp cuts to the Medicaid government healthcare program for the poor, and from conservatives unhappy it did not do enough to erase 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.
Trump pledged on the campaign trail last year to overturn Obamacare but also promised nobody would lose coverage.
"I think we're going to get at least very close. I think we're going to get it over the line," Trump said a day after meeting with most of the Republican senators to urge them to break the impasse.
Trump said later the legislation was moving along well and predicted a "big surprise" was yet to come, without elaborating.
Obamacare 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.
Showing the conflicting demands for changes to the bill, Senator Rand Paul, a vocal conservative opponent of it, 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 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.
(Additional reporting by Susan Heavey, Susan Cornwell, Steve Holland, Mohammad Zargham, Tim Ahmann and Jeff Mason; Writing by Frances Kerry; Editing by Will Dunham)