Counihan said he expected the new CBO report to show an even bigger drop in the number of insured Americans than had been previously projected.
If that is the case, Counihan said, getting the bill passed by the Senate "becomes more problematic" because it will "re-energize" public opposition to the unpopular bill.
"But I think [the bill] is problematic to begin with," he added.
Earlier CBO reports on prior versions of the same bill estimated that 24 million more people would be uninsured by 2026 if it becomes law than would the case if the Affordable Care Act remained in effect. Most of those coverage losses would come in 2018, when 14 million more people would become uninsured, the reports found.
The projected drops in coverage result from the elimination of Obamacare's rule requiring most people to have some form of insurance or pay a tax penalty, as well as expected higher premiums due to the new law. Later reductions in numbers of uninsured people stem from changes made to how people are subsidized for purchasing individual plans, and reductions in federal support for Medicaid.
The CBO also projected that in 2018 and 2019, average premiums for individual plan would be an average of 15 to 20 percent higher than they would be under Obamacare. Again, that would result from elimination of the Obamacare mandate requiring people to have insurance.
However, "by 2026, average premiums for single policyholders in the nongroup market would be roughly 10 percent lower than under current law," CBO said.
That does not mean that premiums would be 10 percent lower than what they currently are.
The new report — which will be the third CBO analysis of the bill — will factor in the effects of a major amendment tacked onto the legislation that helped win approval for it from conservatives in the House.
The so-called MacArthur amendment would allow states to apply for waivers from the federal government to let insurers charge people with pre-existing health conditions higher premiums for their plans than healthier people. Obamacare currently prohibits such discrimination. States that applied for the waivers would have to operate "high-risk pools" or other programs that would offer coverage to people with pre-existing conditions who faced being priced out of the individual market.
The same amendment also would let states seek waivers for rules mandating that insurers offer a certain minimum set of "essential health benefits" in their plans.
Craig Garthwaite, an associate professor for the Kellogg School of Management at Northwestern University , said he expects "maybe there's going to be a slight decline in the number of uninsured people" in the new CBO report compared with the prior reports.
But Garthwaite does not expect any such change to significantly affect the debate over the Republican bill.
He said he has told friends that even if the number of people who would become uninsured under the new bill is cut in half, it would still be in the "double-digit" millions, and risk political blowback.
Obamacare, despite itself being controversial, is credited with expanding health coverage to 20 million Americans since 2010, reducing the uninsured rate to around 9 percent of the population. When President Barack Obama signed the ACA into law in 2010, the uninsured rate stood at 16 percent.
Garthwaite said there might be a "slight decline in the premium" prices in the new CBO report relative to the prior reports.
"But again, you're going to get those premiums from covering less" benefits and people, Garthwaite said. "If I buy a crappier car, I pay less."
Garthwaite said CBO analysts have "a Herculean task" in the new report, because they will have to project how many states will apply for a waiver under the MacArthur amendment, and how the insurance markets in those states would be affected if waivers are granted.
"They're going to make some guesses," he said. "I think it's really hard to have a lot of confidence" in the related projection based on those guesses, he said.