The operation to get the votes is in overdrive at this point as leaders try to secure 50 as soon as possible so they can come back after the July 4 recess, get a new score from the Congressional Budget Office, pass a bill and move on to the rest of their agenda. There are still questions as to whether Republicans will have a new draft by the time they leave Friday.

"I don't really know," said Sen. Roy Blunt, a member of the GOP leadership. "It's possible."

Republican senators seem more optimistic than they were Tuesday when McConnell scrapped plans to vote on the legislation this week, but the divisions between conservatives and moderates are still visible. Moderates still want to reverse Medicaid cuts in the Senate bill and conservatives are urging leaders to give states more freedom to roll back Obamacare insurance regulations.

Unlike President Donald Trump who sticks to applause lines and sweeping promises of success when it comes to health care, Verma is an administration source Republican members trust to dig in. In the House, she was a closer, playing an indispensable role in getting members to vote yes.

The thinking in the Senate is she can do the same: assuage concerns and use administrative power to get Republicans over the hump.

On Wednesday she met with moderate Alaska Sens. Lisa Murkowski and Dan Sullivan, West Virginia's Shelley Moore Capito and Nevada's Dean Heller -- all who have expressed concerns with the Senate bill and hail from states that expanded Medicaid.

Verma also attended the Senate Republicans' policy lunch.

Members said Verma was helping with damage control after the CBO estimated that 15 million Americans would lose Medicaid over the next decade if the Senate passed its bill.

"She's just there with her numbers and looking at kind of broad based numbers. I think the data is really really important," Sullivan said leaving his meeting with Verma. "You know we had our lunch the other day with the CBO and you know they do important work, but it's not like the 10 Commandments coming down from Mt. Sinai. There's a lot of assumptions. A lot of assumptions that go into their estimates and some of 'em are a little bit, you know, speculative."

Trump, for his part, mentioned health care several times Wednesday, and as his habit, without specifics.

"We're going to have a big surprise," Trump said in the Oval Office during a photo op with the Chicago Cubs. "We're going to have a great, great surprise."

But Verma cannot solve all the Senate's problems.

Conservatives still want to make sure that the Senate health care bill includes more Obamacare regulation repeals. The administration could make some of those accommodations, but one GOP aide warned that "would all be temporary."

A number of Republican senators including Sen. Susan Collins of Maine and Sen. Bob Corker of Tennessee have also said they want to bolster the amount of money the federal government gives low-income individuals to help buy health insurance. Corker, specifically, said after a meeting in McConnell's office that he was not comfortable rolling back a net investment tax for the wealthy while low-income people may be set back with the GOP health care bill.

"That's not an equation that's appropriate," Corker said adding that he thought leadership may address the concern.

Keeping that tax in place and increasing the subsidies, however, could be a nonstarter for conservatives.

In many ways, Wednesday was just a repeat of the negotiations of weeks past with no sign that any member is ready to give much ground at this point.

Collins -- a member who announced she wouldn't support the last version of the Senate's health care bill-- told reporters Wednesday's Republican lunch was a "full and frank" discussion on health care with Republicans still trying to sort out their differences.

"I personally think it's going to be difficult to do so, but you never know," she said of leadership's desire to reach a deal by Friday.

After her meeting, Capito raced from reporters but indicated she is still undecided and needs to think about what she heard.

"Have to see when a final bill comes out," she said. "I'm in a moment of silence. ... Silence is golden for right now."

CNN's Phil Mattingly, Sam Kessler, MJ Lee, Manu Raju, Jeremy Diamond and Ted Barrett contributed to this report.

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More optimism than progress for Senate health care bill - CNN