* McConnell meets Republican senators, seeking path forward
* Key senator says goal is to work out changes by Friday
* Trump spurns Schumer proposal for meeting of all senators (Recasts with more McConnell meetings, Trump comments)
WASHINGTON, June 28 (Reuters) - The top U.S. Senate Republican struggled on Wednesday to salvage major healthcare legislation sought by President Donald Trump, meeting privately with a parade of skeptical senators as critics within the party urged substantial changes.
A day after Senate Majority Leader Mitch McConnell abandoned plans to seek passage of the bill this week after it became clear he lacked the needed 50 votes, Republican leaders set a goal of Friday to work out changes so it can be taken up after lawmakers return from next week's Independence Day recess.
Undoing the 2010 law known as Obamacare, Democratic former President Barack Obama's signature legislative achievement, has been a seven-year Republican quest and was a top campaign promise last year by Trump. But intra-party policy differences have tripped up the effort, leaving the fate of the legislation to repeal major parts of Obamacare in doubt.
Acknowledging demands from fellow Republicans for increased 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. At least 10 Republican senators - including moderates, hard-line conservatives and others - have expressed opposition to the current bill, although some have said they want to vote for it if certain changes are made.
McConnell, with his reputation as a strategist on the line, 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 concerns about the bill or was undecided.
NEW CBO SCORE TO COME
Cornyn said it would be "optimal" to have changes to the legislation worked out by Friday so 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 medical insurance over a decade while cutting the federal deficit by $321 billion.
The balancing act for McConnell is fashioning legislation that moderates and conservatives in his party can embrace.
The prospect of so many people losing insurance is unpalatable to moderates such as Senator Susan Collins, a key opponent of the draft legislation. She said it would be "very difficult" to reach agreement on the bill by Friday.
Trump rebuffed a proposal by Senate Democratic leader Chuck Schumer for the Republican president to call all 100 senators to the Blair House, across the street from the White House, to craft a bipartisan healthcare bill to fix, not gut, Obamacare. Trump said he did not think Schumer was serious.
The bill drew protesters, including cancer survivors and people with disabilities, to the offices of several senators, trying to convince them to reject the Senate bill. Capitol Police said they had arrested 40 people on charges of crowding and obstructing the offices.
Obama's 2010 Affordable Care Act, which passed without Republican support, has expanded health insurance coverage to some 20 million people but Republicans call it a costly government intrusion.
Schumer and other Democrats have repeatedly said talking about a repeal of Obamacare is a non-starter, they have expressed willingness to discuss ways to improve it.
Trump said the Senate legislation was moving along well and predicted a "great, great surprise" but did not elaborate.
The Senate legislation would roll back Obamacare's Medicaid expansion, cut planned Medicaid spending starting in 2025, repeal most of Obamacare's taxes, end a penalty on Americans who do not obtain insurance and overhaul Obamacare's subsidies that help people buy insurance with tax credits.
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, Richard Cowan, Susan Cornwell, Steve Holland, Jeff Mason, Mohammad Zargham, Tim Ahmann and Jeff Mason; Writing by Will Dunham and Frances Kerry; Editing by Bill Trott)