McConnell was unveiling his plan even as GOP senators from across the party's political spectrum complained about the package and the secretive, behind-closed-doors meetings he used to draft a measure reshaping the country's medical system, which comprises one-sixth of the US economy.
"It will be different and...take a different approach based upon these endless discussions we've had with the only people interested in changing the law, which is Republican Senator", said Senate Majority Leader Mitch McConnell.
"No one knows the Senate better than McConnell", one White House official said when asked about Trump's involvement, an acknowledgment that he is taking the lead. Its goal is to repeal and replace the Affordable Care Act-former President Obama's signature legislation.
"I want to assure you, before this summer is over".
McConnell's ability to line up votes is considered masterful, and he's eager to pass legislation fulfilling a keystone campaign promise of President Donald Trump and countless GOP congressional candidates.
An estimated 23 million people could lose their healthcare under the House plan, according to the non-partisan Congressional Budget Office.
A bill that toughens sanctions on Russian Federation in the wake of the Kremlin's efforts to disrupt the 2016 presidential election sailed through the Senate with a huge 98-2 majority last week, but it has run into a roadblock in the House of Representatives.
Russian fan leader banned from opening Confederations Cup match
Russia, a record low 63rd in FIFA's world rankings, face Portugal on Wednesday and New Zealand play Mexico the same day. It helped the Russian team to seize the lead after twice having shots stopped on the line.
There was even stronger opposition to the provision in the House bill that would allow insurers to charge older customers of individual health plans much more than younger people than is now allowed by Obamacare.
Democrats said they will use procedural tactics to slow the Senate's work in an effort to focus attention on the Republican effort. "What I've told leadership very clearly is I'm going to need time and my constituents are going to need time to evaluate exactly how this is going to affect them", he added.
How do GOP senators know the president - just as he did after the House bill - won't reject it as too "mean" and thereby hang senators out to dry?
Senator Susan Collins, a moderate Republican from ME, said she wants to read an assessment by the nonpartisan Congressional Budget Office (CBO) on its impact on cost and insurance coverage before making her decision. The bill will be brought to the Senate floor once the CBO has assessed its cost and impact, "likely next week", McConnell said.
Besides Lee, two other conservatives were also complaining. Thune said "it's high time we turned the page on this failed Obamacare experiment".
Kentucky Sen. Rand Paul said that the legislation should be debated "in the open".