The House bill to repeal and replace ObamaCare would reduce the federal deficit by about $2 trillion over 20 years, according to a rough estimate released Monday by the Committee for a Responsible Federal Budget (CRFB).

The estimate from the nonpartisan budget watchdog comes ahead of Thursday's planned House vote on the measure. The bill has the support of the White House and House GOP leadership, though some conservative and moderate GOP lawmakers oppose it.

The American Health Care Act (AHCA) would repeal ObamaCare's mandates and most of its taxes, and create new tax credits that people could use to buy health insurance. It also would end the Medicaid expansion and provide federal funds for Medicaid on a per-capita basis.

The Congressional Budget Office (CBO) estimated that the bill would produce savings of $337 billion over a decade, and it said that the bill wouldn't increase the deficit outside of the 10-year budget window. But the CBO hasn't yet provided an estimate of the savings the legislation would produce in its second decade of enactment.

It did, however, project that the number of people without health insurance would grow by 14 million in 2018, rising to 24 million in a decade.

The CRFB estimated that the bill would reduce the deficit by $1.6 trillion between 2027 and 2036, so the bill would lead to savings of about $2 trillion in its first two decades. Including interest savings, the bill would reduce the deficit by $2.4 trillion over 20 years and would lower the debt in 2036 by 6 percent of gross domestic product, the group added.

Deficit reduction would be greater in the bill's second decade than in its first because the savings would be phased in during the first 10 years, spending on the bill's tax credits would likely grow more slowly than spending on ObamaCare's credits and subsidies, some of the costs in the new bill would be temporary, and the per-capita caps on Medicaid would likely grow more slowly than the current Medicaid program, the CRFB said.

However, it warned that there are uncertainties with its estimate and said, "It is also worth noting that the AHCA's long-term savings could be significantly lower if various temporary policies were continued."

For example, under the bill the "Cadillac tax" on high-cost healthcare plans is delayed until 2025. If it were repealed for longer than that, as is likely since the tax is disliked by both Democrats and Republicans, net savings from the bill could be reduced by $600 billion over 20 years. Future congressional efforts to avoid smaller tax-credit and Medicaid payments could also cut into to the amount of savings, the CRFB said.

"In other words, while the AHCA would save significant money over time, it could also create pressure to spend this savings like the [Affordable Care Act] did," the CRFB wrote. "We hope that as policymakers amend and adjust the AHCA, they continue to work to generate long-term debt reduction and to do so in a sustainable way that also helps to slow health care cost growth."

The CRFB's estimate did not take into account expected changes to the bill that would allow states to have the options to impose work requirements on Medicaid recipients and to receive block grants for Medicaid. The CBO may not produce an updated "score" of the bill before the House votes.