Story highlights Republicans have been working on a Senate version to repeal and replace Obamacare

Democrats have been making public pushes to get more information from GOP plans

(CNN) Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer engaged in dueling statements on Friday over health care, one day after the two men expressed hope of more cooperation in a joint interview.

The two leaders struck a tone of bipartisanship in a joint interview with CNN's Anderson Cooper Thursday night at the Congressional Baseball Game, though they stressed they still had their policy differences.

Those differences were amplified Friday when Schumer sent a letter Friday requesting an all-senators meeting in the Old Senate Chamber next week.

Senate Democrats have been blasting Republicans for deliberating the health care bill behind closed doors, saying they've only been learning of the ongoing negotiations through media reports.

"Please accept our invitation to sit down together in the old Senate Chamber so we can hear your plans and discuss how to make health care more affordable and accessible in the United States," Schumer writes in the letter to Senate Majority Leader Mitch McConnell, which was sent to the press by Schumer's office.

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