Last Updated May 4, 2017 9:17 PM EDT
The early reaction from Senate Republicans to the House passage of the American Health Care Act (AHCA) to repeal and replace Obamacare signaled they're likely to make changes to the House bill.
The chairman of the Senate Health, Education, Labor & Pensions Committee suggested that GOP senators could even pitch their own legislation to dismantle the Affordable Care Act.
"I congratulate the House on passage of its bills. The Senate will now finish work on our bill, but will take the time to get it right," Sen. Lamar Alexander, R-Tennessee, said in a statement.
The goals for the Senate bill, he said, include lowering premium costs, rescuing Americans trapped in the Obamacare exchanges, making sure those with pre-existing conditions have access to insurance and gradually giving states more flexibility with Medicaid.
Senate Majority Leader Mitch McConnell's, R-Kentucky, office said that the upper chamber will consider the measure once budgetary and procedural scorekeeping reviews are completed. The House passed the latest GOP-sponsored version of the bill Thursday afternoon without a new score from the nonpartisan Congressional Budget Office (CBO).
Still, McConnell praised it as "an important step."
"We are now closer to giving our constituents freedom from the increased costs, diminishing choices, and broken promises of Obamacare," he said in a statement.
He added that the status quo is "unacceptable," but McConnell's statement didn't say whether the Senate would take up the House bill. The Senate has to first review whether the House measure complies with budget reconciliation rules, which allow for a simple majority of senators to pass a bill rather than a supermajority. If the Senate crafts a different version, it will have to be reconciled with the House.
While other Senate Republicans stopped short of explicitly embracing the bill in its current form, they applauded their House counterparts for moving forward.
"I don't know what's in it," Sen. Lindsey Graham, R-South Carolina, said. "I'd be curious about the Medicaid provisions. South Carolina chose not to expand Medicaid which I thought was responsible. My test will be: is it good for the people of South Carolina? And is it good for the nation? I have no idea yet."
But Graham also criticized the House for rushing the measure to the floor.
"The bill has been out for less than 24 hours," Graham said. "No amendments. Debates for three or four hours. Any time you have a process like this that hasn't been scored you've got to be suspicious of the outcome."
Sen. John McCain, R-Arizona, said he thinks Congress needs to "reach a conclusion," but he also disapproved of the House decision to vote on the bill before a CBO score had been issued.
"I don't approve of it, but whatever they want to do. They spend their time criticizing me, but I won't," he said.
Sen. Bill Cassidy, R-Louisiana, said "it will be weeks to get a score" and Sen. Rand Paul, R-Kentucky, said that the Freedom Caucus made the bill "a lot less bad."
"That's the nicest thing I could think to say," Paul said. "Part of my problem with the bill is that the underlying premise of Obamacare is that the federal government for the first time would buy insurance for people. That fundamental premise of Obamacare is kept."
CBS News' Walt Cronkite contributed to this report.