Washington (CNN) Florida Republican Rep. Brian Mast left Washington last week undecided about the GOP health care bill to repeal and replace much of Obamacare.

Fortunately, he had a ride home to the Sunshine State: Air Force One.

Mast got to discuss his concerns about how the bill would impact the large senior population in his district directly with President Donald Trump and White House chief of staff Reince Priebus on the flight down to West Palm Beach.

"It's definitely moving in the right direction," Mast told CNN on Monday, adding he is now a "lean 'yes'" on the bill.

"They are asking us: What do you think? What does it take to get you to 'yes'?" Mast said.

Mast is one of several Republican lawmakers that Trump, House Speaker Paul Ryan and other GOP leaders are targeting as they try to secure the 216 votes they need to pass their health care bill Thursday.

Trump is making calls to individual members, according to GOP aides, and will personally address the full House GOP conference on Tuesday morning. House Republican leadership aides make clear that it will be up to Trump to close the deal with the most conservative members of the conference.

While conservatives from the House Freedom Caucus are the ones on cable TV loudly and repeatedly slamming the bill, Trump and Ryan are looking elsewhere.

Already, instead of the kind of wholesale rewrites that the hard-right wants, Ryan, White House officials and Health and Human Services Secretary Tom Price have concentrated on trading more targeted changes proposed by members for their support, according to multiple House GOP leadership sources.

Centrist Republicans have been in frequent contact with leaders and the whip operation and are quietly exerting their own influence.

Late Monday, Ryan unveiled his final changes to the measure. They would make additional changes to Medicaid that were pushed by conservative members, such as giving states the option of requiring able-bodied Medicaid recipients to work. Another change would allow states to opt to receive federal Medicaid funding as a block grant.

But many on the right lobbied hard to speed up the date when the Medicaid expansion to the states would be halted. That was too far for House and Senate moderates, along with some of the governors administering the program, and the idea was set aside.

Ryan and company still have work left to do.

"I am still a 'no' on the bill," Florida Republican Rep. Ileana Ros-Lehtinen told CNN, saying that a high number of her constituents across all age groups who rely on subsidies in the current law will see less support under the GOP bill. She added that she's no fan of Obamacare and the impact it's had on her district, but, "this Republican plan makes the wound that much deeper and harder to heal."

New Jersey Rep. Leonard Lance told CNN that "I'm a lean 'no.'" When pressed if any of the new changes could get him to back the bill he replied, "I doubt it."

Members of the moderate "Tuesday group" are expected to head to the White House on Tuesday. GOP Rep. Brian Fitzpatrick, who represents a district outside Philadelphia, posted on his Facebook page that he couldn't vote for the bill.

"I have many concerns with this bill, and first among them is the impact on the single most important issue plaguing Bucks and Montgomery Counties, and the issue that I have made my priority in Congress: opioid abuse prevention, treatment and recovery," Fitzpatrick wrote.

In an effort directly targeting centrist Republicans from upstate New York, leaders added a provision designed to transfer more Medicaid dollars from the county level to the state level. New York Rep. Chris Collins told CNN the change would help bring along other members of his state's delegation who are currently wavering on the bill. The change would apply to New York State only, a GOP aide said.

It's not just moderates who are still wavering. Rank-and-file members still have concerns that the reconciliation package will make health care insurance more expensive for those over 50. Once the Congressional Budget Office report made it clear this group's premiums could increase, the message to leaders was clear: That needed to be fixed before the House vote.

Ryan signaled on a Sunday talk show that they heard those concerns, saying "we agree, we believe we should have even more assistance. And that's one of the things we're looking at for that person in the 50s and 60s because they experience higher health care costs."

On Monday several House Republicans told CNN that amendments crafted by GOP leaders would pave the way for the Senate to craft more generous tax credit for those aged from 50-64.

House Majority Leader Kevin McCarthy told CNN "we've listened to all the different concerns."

McCarthy explained that the House bill will include a provision allotting resources so that the tax credits can be more generous for those aged 50-64, but noted "the Senate will write the policy" because of procedural issues. He stressed that House GOP members recognize that this change will be part of the final package and added "there's a lot in this of what they've been asking for."

Conservatives say they're not sold as well

Mast wasn't the only lawmaker in Florida.

Rep. Mark Meadows, R-North Carolina, the chair of the House Freedom Caucus, flew to Mar-a-lago over the weekend to huddle with top White House officials and Sens. Ted Cruz and Mike Lee, two leading Senate critics of the bill.

Their efforts to get larger changes to the bill were rejected, aides say. A White House meeting with senators Monday also left conservatives unhappy.

The leadership and White House has made the calculation that a bloc of those in the Freedom Caucus would never be satisfied, and any further effort to pull the bill to the right would erode support in the middle. Republican leaders believe Trump's stamp of approval, plus his personal pitch, will help get them more votes on the right, especially since the President won many of the districts represented by Freedom Caucus members by bigger margins than they did.

"I don't think the majority of the Freedom Caucus members are eager to see President Trump fail; that would be a risky move for them to make," one of these senior GOP aides told CNN, suggesting that leaders are banking on a chunk of votes from the group to come through after some additional outreach by the time the vote comes on Thursday.

But Freedom Caucus members aren't giving in yet, and say they have the votes to block the measure.

Rep. Raul Labrador, R-Idaho, acknowledged that with Trump's visit Tuesday morning, "there's going to be a lot of pressure, and we all respect Trump and we want to work with him."

But, Labrador said, "We don't believe that they have 216 votes. In fact, we know that they don't have 216 votes."