Senate Republicans are planning to vote next week on their bill to repeal and replace ObamaCare, according to Sen. John Barrasso John Anthony BarrassoSenate to push funding bill vote up against shutdown deadline The conservative case for phasing out hydrofluorocarbons GOP senator attacks Biden: 'I'm not sure what he recalls' MORE (R-Wyo.).

"I believe we’re going to vote before the Fourth of July recess on a healthcare plan, a repeal and replacement of ObamaCare," Barrasso, a member of GOP leadership, said on Fox News.

"Every Republican is trying to get to yes," Barrasso said while noting, "There are some differences of opinion on specific details of this."

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The vote by the end of the month was expected, as 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.) wants to move quickly on healthcare and get on to other issues.

The timeline is fast, though, given that lawmakers and the public have not yet seen the text of a bill. That could come later this week.

Republicans have already sent pieces of a bill to the Congressional Budget Office, but the CBO will have to issue an analysis, known as a score, once the bill comes together.

It remains unclear if Republicans have the votes to pass the bill. There is no deal yet on a range of contentious issues, ranging from phasing out ObamaCare's Medicaid expansion to repealing pre-existing condition rules.

Senate Republicans are considering even deeper cuts to Medicaid than the House bill, which could repel some moderates.