(CNN) The bipartisan Senate Obamacare stabilization bill would reduce the deficit by $3.8 billion over the next decade and would not substantially change the number of people with health insurance, the nonpartisan Congressional Budget Office said Wednesday.

The bill, authored by Republican Sen. Lamar Alexander of Tennessee and Democratic Sen. Patty Murray of Washington, would fund Obamacare's cost-sharing subsidies for the next two years, while providing more flexibility to states to adapt the health reform law's regulations to their needs. It would also open up "copper" plans, which have lower premiums but higher deductibles, to enrollees older than age 30, while requiring the Trump administration to spend $106 million on outreach and enrollment assistance in 2018 and again in 2019.

President Donald Trump announced earlier this month that he was ending federal support for the subsidies, which reduce deductibles and co-pays for lower-income enrollees.

Trump has sent mixed messages on the Alexander-Murray bill. Senate Majority Leader Mitch McConnell has signaled openness to putting it on the Senate floor for a vote if Trump gives his blessing.

"The White House has the ball," Alexander said Tuesday . "I think it's up to the White House to take the suggestions, work with Senate and House leaders, and come up, and decide, what the President would like to do."

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