(CNN) When it comes to the Graham-Cassidy health care bill, there is one thing Republicans agree on right now: It's their last shot to repeal and replace Obamacare.

That may be all the motivation they need to pass it.

In recent days, an intense operation to sell the bill to few key holdouts has gotten underway. But most of those conversations are happening under the radar.

On Wednesday, the bill's sponsors, Sens. Lindsey Graham of South Carolina and Bill Cassidy of Louisiana, briefed Alaska Sens. Dan Sullivan and Lisa Murkowski. Arizona Sen. John McCain, another holdout, is also under pressure to get to "yes," with Graham, a close friend, taking the lead on trying to convince him.

One White House official stressed that leaning on Graham wasn't a bad thing, adding: "I wouldn't say that's all we're relying on. Lindsey has good relationships that we can leverage."

By and large, however, many Republicans seem to be shrugging "yes" to Graham-Cassidy, a health care bill that was released a week ago and would repeal the individual and employer mandates and turn the federal funding for Medicaid expansion and the subsidies into a block grant program.

And in large part, it's because time is running out. According to the chamber's parliamentarian , senators only have until the end of the month to pass a bill with just 51 votes under the procedure known as reconciliation, and the Senate's last-ditch exercise isn't all that different than the one that ultimately resulted in a health care bill being passed in the House.

"You know, I could maybe give you 10 reasons why this bill shouldn't be considered," Iowa Sen. Chuck Grassley told local reporters, according to The Des Moines Register. "But Republicans campaigned on this so often that you have a responsibility to carry out what you said in the campaign. That's pretty much as much of a reason as the substance of the bill."

So far, the full-fledged public airing of grievances that once dominated the Senate process isn't nearly as visible. Conservatives and moderates aren't openly sparring -- although deeply divided over cuts to Medicaid, the size of insurance subsidies and whether or not to keep Obamacare taxes. Some notable Republicans are even papering over concerns, crossing red lines they once set for themselves in the name of getting something -- anything -- across the finish line.

If they have concerns, they are bringing them to leadership quietly. Vice President Mike Pence is taking the lead on affirming some of the softer "yes" votes, a senior adviser said. And, President Donald Trump doesn't seem to have any concerns about the policy of Graham-Cassidy as long as it gets him a legislative win.

"I hope Republican Senators will vote for Graham-Cassidy and fulfill their promise to Repeal & Replace ObamaCare. Money direct to States!" he tweeted Wednesday morning

I hope Republican Senators will vote for Graham-Cassidy and fulfill their promise to Repeal & Replace ObamaCare. Money direct to States! — Donald J. Trump (@realDonaldTrump) September 20, 2017

The race to the finish line, however, gives members both the distinct advantage and danger of not fully knowing how the bill will affect one-sixth of the economy. If they do vote next week, senators are expected to bring Graham-Cassidy to the floor without having a full Congressional Budget Office assessment that estimates how many Americans would lose coverage, something many dismiss now as unnecessary.

"We have more than enough information," Sen. Ron Johnson, a Republican from Wisconsin and a co-sponsor of Graham-Cassidy, said about not having a CBO score. "We've been highly disappointed in how CBO has really conducted themselves throughout this health care process."

One big advantage of Graham-Cassidy is that the bill outsources many of the toughest decisions about health care -- what to prioritize, how to regulate the marketplace and cover health care for the poor -- to the states. Graham-Cassidy allows individual senators to imagine health care policy in their own image even if outside groups have warned a number of states -- some even led by Republicans -- would lose federal dollars if the bill passes.

The rapid pace of the bill, however, has left the party vulnerable to criticism even among its own members.

McCain has said the expedited process is deeply disturbing. And Republicans -- at times -- have had a tough time managing the public perception about a bill they haven't had time to craft a message on.

And ask almost any senator how the bill affects their state, and many admit they are still grappling with complex data.

"Digging, digging, digging," Sullivan said Tuesday afternoon.

Seema Verma , the administrator for the Centers of Medicare and Medicaid, has been tasked primarily with getting members answers when they need them. But outside analysis from groups like Avalere that show states like Alaska, Arizona and Ohio losing money under Graham-Cassidy aren't making it easier for members to vote "yes."

Wyoming Sen. John Barrasso, a member of the Republican leadership and a doctor, also made headlines after telling NBC's Katy Tur that "there shouldn't be" a requirement for insurers to cover essential health benefits.

Essential health benefits include things like maternity care, substance abuse treatment, hospitalization and prescriptions and became popular under Obamacare.

"There are not protections for essential health benefits in this bill," MSNBC host Katy Tur began in an interview earlier this week.

"And there shouldn't be," Barrasso said, explaining that they increased prices of insurance.

On Capitol Hill, Republicans seem to be most concerned with getting a vote at the moment. The rest they can understand later. Former hill staffers and lobbyists warn that's a dangerous game, however.