(Fixes attribution of quote in 10th paragraph to Senator Corker from Senator Rounds)
* 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
By Susan Cornwell and Yasmeen Abutaleb
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.
Republican leaders hope to agree on changes to the legislation by Friday so lawmakers can take it up after next week's Independence Day recess.. Senate Majority Leader Mitch McConnell on Tuesday abandoned plans to seek passage of it this week because Republicans did not have 50 votes to pass the bill.
For seven years, Republicans have led a quest to undo the 2010 law known as Obamacare, Democratic former President Barack Obama's signature legislative achievement. Trump made dismantling it a top campaign promise during last year's presidential campaign but policy differences within the party have raised doubts Republicans can achieve a repeal.
Democrats have unified against the bill and Republicans control the Senate by a slim 52-48 margin, which means McConnell can afford to lose only two Republicans. So far at least 10 - including moderates and hard-line conservatives - have expressed opposition to the current bill, although some indicated they would vote for it with certain changes.
McConnell, with his reputation as a strategist on the line, met with a procession of Republican senators in his office on Wednesday. John Cornyn, the No. 2 Senate Republican, said party leaders will talk to every Republican senator who has concerns about the bill or is undecided.
The House of Representatives passed its healthcare bill last month, only after striking a balance between the center of the party and the right wing. Now McConnell must find a similar sweet spot.
During a lunch meeting on Wednesday Republicans made presentations on potential fixes. Senator Rand Paul called for jettisoning more parts of Obamacare to get conservatives on board.
TAX ISSUE
Senator Mike Rounds suggested keeping a 3.8 percent Obamacare tax on high earners' investment income, which the current bill would eliminate. Rounds said the tax could pay for more Americans to receive the tax credits that help pay for health insurance.
Senator Bob Corker, who also supports keeping the tax, said one of the issues he was focused on was helping lower-income Americans pay for health plans.