Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellDemocratic senator to party: 'A little message discipline wouldn't kill us' House to vote on resolution affirming peaceful transition of power Republican lawyers brush off Trump's election comments MORE (R-Ky.) said Republicans would see a "discussion draft" of healthcare reform legislation on Thursday.

McConnell said reporters will get a chance to see the bill then as well, addressing complaints from Democrats that GOP leaders have kept the bill secret.

He said the legislation will move to the floor next week, as soon as lawmakers get a cost estimate and analysis from the Congressional Budget Office.

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When asked how long lawmakers will have to review the legislation, the majority leader vowed that they would have "plenty of time."

"I think this will be as about as transparent as it can be," he said.

Earlier in the day, moderate Republicans such as Sens. Susan Collins Susan Margaret CollinsDemocratic senator to party: 'A little message discipline wouldn't kill us' Poll: 57 percent of Americans think next president, Senate should fill Ginsburg vacancy On The Trail: Making sense of this week's polling tsunami MORE (Maine) and Shelley Moore Capito Shelley Wellons Moore CapitoCongress must finish work on popular conservation bill before time runs out Second GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure MORE (W.Va.) said they are still concerned about changes to Medicaid that would curb federal spending.

Republicans may vote on the bill as soon as next week.