Senate Majority Leader Mitch McConnell on Thursday re-launched his bid to overhaul chunks of ObamaCare, unveiling a revised bill with concessions to conservatives and moderates alike – though key senators already have voiced opposition.

The new plan, significantly, includes a provision based on a proposal by Sen. Ted Cruz allowing insurers to offer lower-cost, bare-bones policies.

The Texas Republican said in a written statement he is "encouraged that the revised bill ensures consumers have the freedom to choose among more affordable plans that are tailored to their individual healthcare needs."

WHAT TO KNOW ABOUT THE SENATE HEALTH CARE BILL

The change could help sway fellow conservatives, while also making the job of attracting moderates more difficult. Once again, McConnell faces an uphill climb in stitching together a fragile coalition in his own party to even bring the bill to the floor, after a similar bill was sidelined in the face of political headwinds last month.

“We need to bring this thing to closure,” Republican Sen. John Thune of South Dakota said Thursday on Fox News’ "America’s Newsroom." “Get it to the finish line. And be able to get something on the president’s desk that will rescue people from a failed ObamaCare system that has markets collapsing and rates going through the roof.”

The revamped provisions of the health care bill were released to rank-and-file members of the Senate in a closed-door session Thursday morning.

The primary revisions, according to Republicans, include a change to allow people to use Health Savings Accounts to pay for premiums; an additional $45 billion for substance abuse treatment to combat the opioid epidemic; the ability for people in the individual market to purchase a lower-premium health insurance plan and an additional $70 billion to encourage state-based reforms.

The new package would keep most of the original bill's Medicaid reductions. But it would retain Obama tax increases on upper-income people and use the revenue to help some lower earners afford coverage.

The legislation, however, is on the verge of being stalled as a pair of Republican senators -- Rand Paul of Kentucky and Susan Collins of Maine -- say they plan to oppose a procedural vote, known as a motion to proceed, to start debate on the bill. Ohio Sen. Rob Portman is undecided, a spokesman said.

It takes 51 votes to start debate on legislation. That means McConnell cannot lose any other Republican on this vote and would need Vice President Pence to break a tie.

Collins tweeted after the release of the bill that she is against the motion to proceed because of the “deep cuts to Medicaid." She added that she’s “ready to work” with Republicans and Democrats “to fix flaws” in ObamaCare.

Efforts have also been made to win over conservatives like Paul and other like-minded lawmakers who argue the legislation doesn’t go far enough to repeal ObamaCare.

But Wisconsin Republican Sen. Ron Johnson, another conservative who initially withheld support for the health care bill because of concerns it didn’t go far enough, said Thursday he would vote yes to open debate on the floor.

Pence on Thursday was seen on Capitol Hill, where he is working to convince Republicans to vote for the bill.

Last month, the Senate Republican leadership delayed plans to vote on health care legislation after failing to attract enough votes from inside the GOP caucus. The House passed a health care bill in May.

Under the revised bill, Obama's penalties on people who don't buy coverage would be eliminated and federal health care subsidies would be less generous.

McConnell hopes to have a vote on the legislation next week. An updated score from the Congressional Budget Office on the legislation is expected in the coming days.

Cruz of Texas, a conservative who did not support the previous version of the bill, said Thursday that McConnell incorporated some of his demands, including his Consumer Freedom Amendment and proposal to allow health savings accounts to pay for health care premiums.

“My central focus has always been on lowering premiums,” Cruz told Fox News’ Peter Doocy on Thursday. “I think that's the key to bringing Republicans together, to uniting Republicans and getting this done.”

The Cruz amendment, however, is included in brackets in the legislation, a sign it could ultimately be changed. “The brackets mean that the policy continues to be worked upon as members react to it,” a senior policy Senate staffer said.

The policy aide said the CBO will evaluate two versions of the legislation – one that includes the Cruz text and one that doesn’t.

Cruz’s proposal would let insurers sell plans with minimal coverage, as long as they also sell policies that meet strict coverage requirements set by Obama's 2010 statute. Moderate Republicans have objected to the idea, arguing it would make policies excessively costly for people with serious illnesses because healthy people would flock to the cheaper coverage.

Before he left for his visit to France, President Trump said in a Wednesday television interview that he is anxious for Senate Republicans to come together to pass health care legislation.

TRUMP URGES SENATE TO PASS HEALTH CARE BILL

“I am sitting in the Oval Office with a pen in hand, waiting for our senators to give it to me,” Trump said in an interview with Pat Robertson for CBN’s "700 Club.”

Trump expressed frustration that Republicans are struggling to pass a bill -- especially since they now have a president willing to sign it. If Republicans don’t pass the legislation, Trump said: “I will be very angry about it and a lot of people will be very upset.”

Speaking of McConnell, Trump said: "He's got to pull it off. Mitch has to pull it off. He's working very hard. He's got to pull it off."

Meanwhile, a pair of Republican senators, Lindsey Graham of South Carolina and Bill Cassidy of Louisiana, released their own alternative propals to repeal ObamaCare on Thursday.

Under the Graham-Cassidy plan, federal dollars spent on Obamacare would be block-granted to states; the individual and employer mandate would be repealed; requirements that health insurers would cover pre-existing conditions would be kept; and the ObamaCare medical device tax would be eliminated while other ObamaCare taxes would remain.

“ObamaCare is going to collapse,” Graham said. “Instead of having a one-size-fits-all solution from Washington, we should return dollars back to the states to address each individual state’s health care needs. Just like no two patients are the same, no two states’ health care needs are the same. A solution that works in California may not work in Virginia.”

No Democrats are supporting the legislation and Senate Minority Leader Chuck Schumer blasted the revised legislation on the floor of the Senate.

“From what we are seeing, the new Republican Trumpcare bill

is every bit as mean as the old one – and in one big way it’s even meaner – with the addition of something like the Cruz amendment,” Schumer said Thursday.

Read the full Better Care Reconciliation Act here.

Fox News’ Chad Pergram, Mike Emanuel, Peter Doocy, Kara Rowland and The Associated Press contributed to this report.