Democratic lawmakers have also criticised the bill, arguing it delivers tax cuts for the wealthy at the expense of vulnerable Americans. The CBO numbers calculate a $1 trillion (£730bn) cuts to healthcare funding if the bill passes.
The latest version of the bill was brought to the Senate floor late Saturday night thanks to a 51-49 vote. Two Republicans joined Democrats in opposing the move.
While senators voted to open debate on the bill, it is unclear whether it has enough support to ultimately pass.
Republicans have a small majority in the Senate with 53 seats. With vice-president JD Vance holding the tie-breaker vote, the party can only afford three defectors.
Democratic senators are using chamber rules to force a reading of the nearly 1,000-page bill in an attempt to delay a vote on its passage.
Under Senate rules, lawmakers now have 20 hours allocated to debate the bill. It is expected that Democrats will use all of their time to further delay a vote, while Republicans will try to speed up the process.
Lawmakers could also propose amendments to the bill. If the revised bill passes the Senate, it still must return to the House of Representatives for final approval before landing on the president’s desk.
Trump has pushed for a quick passage of the bill before a self-imposed 4 July deadline, and the White House said a failure to pass it would be the “ultimate betrayal”.
Republican Senator Rand Paul of Kentucky has said he opposes the bill because it raises the US debt limit. Tillis voiced concern that the bill would cost his state billions of dollars in healthcare funding.
Tillis cited the cuts the bill proposes to Medicaid, a healthcare programme that is relied on by millions of elderly, disabled and low-income Americans.
These cuts have become a hotly debated issue on both sides of the aisle.
Democratic Senator Mark Warner told CNN on Sunday that the bill will negatively impact millions. “This is tax cuts for the wealthiest to end up cutting health care, plain and simple,” he said.
Some Republican senators, however, have defended the bill as a needed step for the US government. Senator Markwayne Mullin of Oklahoma told NBC on Sunday that the legislation aims to eliminate fraud, waste and abuse.
He argued that many Americans using Medicaid are not under the poverty line.
“We don’t pay people in this country to be lazy,” he said. “We want to give them an opportunity. And when they’re going through a hard time, we want to give them a helping hand.”