Lee, though, was looking for more robust alterations to the bill, including a full repeal of all regulations included in former President Barack Obama's plan, officially titled the Affordable Care Act, passed in 2010.
The senator's spokesman, Conn Carroll, said Lee blames those regulations including age ratings that prevent insurers from charging seniors much steeper prices than younger patients and essential health benefits that encompass emergency room visits and preventive services for higher premium costs.
After its release two weeks ago, Lee said the legislation was "a missed opportunity and a step in the wrong direction." His outlook didn't improve much after the meeting with White House staff Monday, which the senator said was "terribly frustrating." He will likely vote against the measure, Carroll said.
Lee had been trying to negotiate a more conservative take on the longstanding GOP promise to "repeal and replace" Obamacare. He met for three hours Saturday with White House officials, including chief strategist Stephen Bannon and Chief of Staff Reince Priebus, at Mar-a-Lago in Florida, where Trump golfs most weekends. Lee joined Texas Sen. Ted Cruz and Rep. Mark Meadows, R-N.C., to voice opposition to the health care bill, titled the American Health Care Act.
Lee also met with White House staff last week and visited with Health Secretary Tom Price two weeks ago. His meeting Monday a fourth attempt at reaching an agreement on the bill included Priebus, as well as Andrew Bremberg, an assistant to the president and director of the Domestic Policy Council; Paul Winfree, director of budget policy and deputy director of the Domestic Policy Council; Marc Short, Trump's director of legislative affairs; and Paul Teller, the White House's liaison to House Republicans.
Though it will likely pass in the House with a vote planned Thursday, a handful of GOP senators aligned against the measure could spell its demise.
The plan retains several provisions from Obamacare, including a requirement that insurance companies cover people with preexisting conditions. It also continues to allow parents to keep their children on their plan until age 26.
The Republican plan slashes subsidies that low-income individuals use to pay for insurance in favor of age-based refundable tax credits. Instead of charging a tax fine for not having insurance, the proposal would allow carriers to add a 30 percent premium surcharge for those who drop coverage for a few months and later look to re-enter the market.
Utah's Rep. Mia Love signaled her support for the measure last week during a telephone town hall.
Though she called the bill a "work in progress" with needed adjustments to Medicare, Love defended the plan as a way to provide insurance to those who want it.
"The bottom line is, Obamacare was unsustainable," the Republican congresswoman said.
Love met with Trump on Friday, along with a handful of other Republican representatives, to speak about the health care bill. Trump is expected to address House Republicans on Tuesday at the Capitol.
Sen. Orrin Hatch has applauded the measure, while Rep. Chris Stewart signaled initial support with room for review. He will likely vote in favor of it. It's unclear where Reps. Rob Bishop and Jason Chaffetz come down, though Chaffetz faced backlash for suggesting on March 7 that low-income Americans may face tough choices under the bill between "getting that new iPhone that they just love" and paying for health insurance. He later sought to clarify the comment.