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.

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