WASHINGTON (AP) — Senate Majority Leader Mitch McConnell says he’s ready to unwrap his latest bill repealing much of President Barack Obama’s health care law, with wary conservatives warning Wednesday that they’re watching to make sure it doesn’t stray from their goals.

McConnell, R-Ky., planned to release the revised measure on Thursday, despite no visible signs that leaders have rounded up enough GOP support to win its passage. He says the Senate will begin voting on the legislation next week in a showdown over one of the party’s top priorities — repealing much of Obama’s health care law.

The resurrected legislation will ease some of the initial bill’s cuts in Medicaid, the health insurance program for the poor, disabled and nursing home patients. It is also expected to beef up health insurance subsidies for lower-income people, paid for by retaining a pair of tax boosts Obama’s statute levied on higher earners to help pay for his expansion of coverage.

Conservative Sen. Rand Paul, R-Ky., said he opposed the new measure because it didn’t do enough to uproot Obama’s law, would increase spending by shoveling billions to insurance companies and keep some tax increases in place.

“I don’t see anything in here really remotely resembling repeal,” Paul, a vociferous foe of McConnell’s initial bill, said of the new version in a conference call with reporters.

Should the Senate pass the legislation — which remains a major question — the House would have to approve it as well. Backing from conservatives in both chambers will be essential because Democrats are united in opposition, and several from the House are already suggesting they’re unhappy with what the Senate might do.

For many conservatives, the key is having provisions allowing insurers to sell low-premium policies with bare-bones coverage, which they say is crucial for reducing premiums. Obama’s law requires policies to cover a list of services including drug abuse services and maternity care, and both bills have language relaxing that requirement.

Conservatives also expressed opposition to the Senate’s likely preservation of Obama’s tax hike on wealthier people. But several suggested it wasn’t a deal-breaker, as long as the new measure also relaxes coverage requirements.