The Congressional Budget Office said it will release an updated score on the House healthcare bill to replace Obamacare on Wednesday.

The updated score will reflect major changes to the House bill, called the American Health Care Act, that was narrowly approved at the beginning of the month. Those changes include a waiver system to let states opt out of certain insurance mandates and adding more money for high-risk pools to cover patients with pre-existing conditions.

An earlier score on the legislation, which guts Obamacare and partially replaces it, said 24 million people could go without insurance over the next decade. It also would reduce the deficit by more than $100 billion over the next decade, CBO said.

Since that score, the legislation changed dramatically. The House approved the bill without an updated score, which rankled many Democrats.

The changes made since the latest score include adding a waiver process that lets states opt out of key insurance mandates including requiring plans to cover essential health benefits and a price control that prevents insurers from charging sicker people more.

The bill also added $23 billion for federal high-risk pools to help cover any sick people who face stiff premium increases.

Deficit reduction is important as Congress is using an arcane pathway called budget reconciliation to get healthcare reform approved in the Senate with 51 votes, instead of the 60 typically required to overcome a filibuster. To use reconciliation, the healthcare bill must affect only spending levels and reduce the deficit by $1 billion in each of the two Senate committees working on the legislation.

The score will play a vital part in the Senate deliberations over its legislation to replace Obamacare. The Senate has largely ignored the House bill and is drafting its own version.

However, several senators have said that the CBO score will influence their work.

The lack of a CBO score was also a key reason the House hasn't sent the bill to the Senate.

A report in Bloomberg News said that there was a chance the bill could come back up for a vote if the CBO score determines the bill doesn't meet the reconciliation requirements.

But House Speaker Paul Ryan downplayed any chance of another vote.

The bill hasn't been sent to the Senate out of "an abundance of caution," he told conservative radio host Hugh Hewitt Friday.