But he said "yes," when asked if Rep. Paul Ryan, R-Wis., should remain as speaker of the House if the bill goes down in flames.
The bill, dubbed the American Health Care Act, has been promoted by Ryan, Trump and other Republican leaders as a tool to undo key sections of the Affordable Care Act, and replace them with new legislation.
Despite the fact that it is a bill pushed by Republicans who control the White House and both chambers of Congress, the plan's biggest threat to passage comes not from Democrats, but from 30 to 40 GOP members of the House who could vote against it.
Some conservatives in the House oppose the bill, or are leaning against it, because it does not go far enough to repeal Obamacare. Moderates have qualms that the bill could lead to steep decreases in the number of Americans with health insurance coverage.
Trump and GOP leaders have offered a series of amendments to assuage concerns of members of Congress. But in doing so, they have may have made it even more difficult to cobble together enough votes to pass it.
Republican leaders postponed the House's scheduled vote for Thursday after it became clear the bill would fail.
Leaders then offered an amendment that would allow states to determine what kind of so-called essential health benefits would be included in health plans, as opposed to the federal government mandating what benefits have to be included.
That change was part of the reason that Frelinghuysen declared himself as a "no" vote on Friday.
"Unfortunately, the legislation before the House today is currently unacceptable as it would place significant new costs and barriers to care on my constituents in New Jersey," Frelinghuysen said in a Facebook post. "In addition to the loss of Medicaid coverage for so many people in my Medicaid-dependent state, the denial of essential health benefits in the individual market raise serious coverage and cost issues."
"I remain hopeful that the American Health Care Act will be further modified. We need to get this right for all Americans," he said.
—Additional reporting by CNBC's Jacob Pramuk