People demonstrate at Trump International Hotel and Tower in New York City, to fight against the proposed changes to the American healthcare system proposed by the Trump Administration and Republicans.

The Congressional Budget Office on Wednesday poured very cold water on the idea that fallout from eliminating Obamacare's key rule could be reduced by passing another pending Senate bill.

The CBO's director said that it would still expect 13 million more people to not have health insurance by 2027 than are currently projected if Obamacare's individual mandate is repealed, even if the Alexander-Murray bill is passed into law.

And the nonpartisan agency also said, again referencing prior projections, it would still expect prices of individual health plans to increase by 10 percent each year above current projections under that scenario.

The CBO's comments in a letter to Sen. Patty Murray, D-Wash., co-author of Alexander-Murray, come as the Senate is contemplating a Republican-sponsored tax bill that would repeal the individual mandate, among other things. That mandate requires most Americans to have some form of health coverage or pay a tax penalty.

Prior Republican efforts this year to repeal much of Obamacare have failed because of concerns it would significantly increase the number of uninsured Americans.

In recent days, a number of Republican senators have suggested that passing Alexander-Murray could reduce some of the impact of repealing the individual mandate, if it is paired with funding of a reinsurance program for Obamacare plans.

Alexander-Murray would restore billions of dollars of federal reimbursements to Obamacare insurers that had compensated them for discounts they must grant low-income customers for out-of-pocket health charges. The Trump administration discontinued those reimbursements last month.

The bill also would give individual states flexibility in setting rules for what kinds of health plans can be sold.

Murray last week had asked the CBO if simultaneously passing the Republican tax bill and Alexander-Murray would change CBO's prior estimates of the effects of repealing the mandate.

CBO Director Keith Hall, in his response Wednesday, noted that last month the agency and the Joint Committee on Taxation had analyzed Alexander-Murray and found that it "would not substantially change the number of people with health insurance, on net."

Nor was the bill projected last month to have any effect on premiums, Hall said.

He wrote that "if legislation were enacted that incorporated both the provisions of [Alexander-Murray] and a repeal of the individual mandate the agencies expect that the interactions among the provisions would be small; the effects on premiums and the number of people with health insurance coverage would be similar to those referenced above."

Hall noted that 4 million more people would be expected to lack health insurance by 2019 than are currently projected if the mandate is repealed. That would increase by another 9 million as of 2027.