Public opposition to the GOP-sponsored House bill to gut Obamacare is growing — even among Republicans.

That increasing unease with the American Health Care Act legislation could spell big trouble for Republican leaders in the Senate, as they prepare to push for passage of their own, still-secret health-care reform bill — which could look quite a bit like the House version.

A new Morning Consult/Politico poll found that half of American voters now say they oppose the AHCA. Back in April, just 37 percent of voters in the same poll opposed that bill.

That is the lowest level of support since the poll began tracking opinion on the legislation.

And while 16 percent of Republican voters opposed the bill in late April, about 30 percent of such voters now say they are against the bill, the Morning Consult/Politico survey found.

Just 35 percent of all voters now approve of the House bill, down from 42 percent at the end of April, according to that poll.

Another survey, also released Wednesday, found that majorities of voters oppose all the key provisions found in the House bill — even in congressional districts that voted strongly for Republicans in recent elections.

Overall, 67 percent of voters in that poll, conducted by the University of Maryland's Program for Public Consultation, oppose the House bill.

The poll asked voters their opinions on seven major parts of the AHCA. Those sections would significantly change, or completely eliminate, key provisions of the Affordable Care Act, as Obamacare is more formally known.

It is not known if all, some, or none of the provisions will be in the draft of the Senate bill to be released Thursday.

But it is expected that there will be at least elements of the provisions in that bill, which Majority Leader Sen. Mitch McConnell, R-Ky., hopes to put to a vote next week.

One part of the AHCA would allow states to obtain waivers that could allow insurers to either not cover people with pre-existing health conditions, or to charge them higher premiums. More than 75 percent of voters oppose that provision, as do about 60 percent of Republican voters, according to the University of Maryland poll.

There was even stronger opposition to the provision in the House bill that would allow insurers to charge older customers of individual health plans much more than younger people than is now allowed by Obamacare.

Eighty percent of all voters oppose that provision, and in deep "red" districts dominated by the GOP, 80 percent of all Republican voters object to that proposed rule.

Majorities of voters in both Democratic and Republican districts questioned for the Maryland poll oppose the AHCA provision that would give states the power to allow insurers to offer health plans that do not include certain minimum health benefits, as well as the provisions that would tend to reduce Medicaid coverage.

Majorities also don't like the repeal of the requirement that large employers offer health coverage to workers or pay a fine, or a provision that would bar Medicaid benefits from being used at Planned Parenthood clinics.

The highest level of support among voters was for a provision of the AHCA that would repeal Obamacare's individual mandate, which requires most Americans to have some form of health coverage or pay a tax penalty. The House will replace that mandate with a financial penalty imposed on people who let their coverage lapse and then renew it.

But support for that provision came from just 44 percent of all voters, compared with 55 percent who oppose it. Even in deep red districts, the provision had only about 50 percent support from all voters.

President Donald Trump, during a meeting last week with Republican senators, reportedly said the House bill was "mean, mean, mean." And during a meeting early this week with tech company CEOs, Trump told them that the Senate bill needed to have more "heart."

In an interview Wednesday with CNBC's "Squawk Alley," Cigna CEO David Cordani was asked whether it matters to the insurer how much "heart" is in the Senate bill, despite the fact that Obamacare health plans represent just a small fraction of Cigna's business.

"It's clear the legislation needs to evolve," Cordani said. "And what we have been able to prove is that if you can engage individuals into health care, and, very importantly, connect with ... physicians and professionals and better-quality health care, then good things happen."