Demonstrators opposed to U.S. President Barack Obama's health-care law, Obamacare, hold signs in front of the U.S. Supreme Court in Washington, D.C., U.S., on Wednesday, March 4, 2015.

Most Americans favor ending Obamacare's requirement that people have health coverage — but a majority opposes the idea after learning how it would affect people and insurance prices, a new poll has found.

The same poll found that relatively few Americans consider a tax reform bill a priority — despite the strong ongoing push by President Donald Trump and congressional Republicans to pass such legislation.

Ranking much higher as priorities for the public are reauthorization of funding for the government's Children's Health Insurance Program, hurricane recovery funding, stabilizing Obamacare marketplaces and addressing a prescription painkiller epidemic.

The Kaiser Family Foundation poll comes as the Senate is considering a tax reform bill that would kill the Obamacare individual mandate. The mandate imposes a financial penalty on Americans who lack health insurance coverage of some kind and who don't qualify for an exemption from the rule.

Repealing the individual mandate would free up almost $340 billion in federal funds that Republicans want applied to tax cuts.

Fifty-five percent of respondents to the poll supported — at least initially — eliminating the mandate as part of a tax-reform bill, according to Kaiser, a leading health policy research group.

Forty-two percent initially opposed the idea.

But the numbers abruptly switched when respondents were "presented with facts and arguments about who is impacted and potential consequences of its repeal," Kaiser said.

About one-third of the supporters of the mandate's repeal — or 20 percent of the public overall — switch to opposing repeal once they hear what could happen.

Sixty-two percent of respondents opposed repeal of the mandate after hearing that most Americans automatically satisfy the rule because they already have health coverage through a job, or from Medicare, Medicaid or another public program.

Sixty percent oppose repeal after hearing it would lead individual insurance plan prices to be 10 percent higher than they otherwise would be if the rule remained in place.

And 59 percent said they opposed repeal after being told that it would lead to 13 million more people being without health insurance over the next decade than are currently projected.

The same percentage opposed repeal when told that no one is penalized for not having insurance coverage if the cost of coverage takes up too much of their income.

It is not clear that the idea of repealing the mandate will survive in the Senate, or in the entire Congress if Senate Republicans manage to pass a bill containing that provision.

GOP leaders in the Senate failed repeatedly earlier this year to pass Obamacare replacement bills that would have ended the mandate. The bills died because a handful of Republican senators worried about the effects of the bills on the number of people with coverage and on insurance premiums.

The Congressional Budget Office has estimated that over the next 10 years 13 million more people would become uninsured and premiums would rise by 10 percent if the mandate were eliminated. CBO also has estimated repeal would reduce the federal deficit by $339 billion. The savings would come from reduced spending on subsidies that lower premium costs for most Obamacare customers.

Just 28 percent of Americans told the Kaiser poll that they viewed tax reform as a top priority for Congress and President Donald Trump.

That is much less than the number — 62 percent — who said the same thing about reauthorizing funding for CHIP, the health coverage program for kids. Congress let CHIP's funding authorization lapse at the end of September, and so far has not approved new money for the program.

Sixty-one percent of respondents viewed hurricane recovery funding as a top priority for Congress and the White House.

And 48 percent said stabilizing Obamacare marketplaces was a top priority.

Just 29 percent of people said that repealing Obamacare was a top priority.

The Kaiser poll was conducted in the past week and questioned 1,201 adults on the telephone. The margin of error for the poll is 3 percentage points.