President Trump wants to make the Republican Party the "party of health care." But a new poll suggests he has a lot of work to do.

In a Politico/Morning Consult poll released on Wednesday, 59 percent of registered voters said they have little or no trust in Trump to protect the U.S. health-care system or make improvements to it. This includes 13 percent who said they have "not much" trust, and 46 percent said they have no trust at all. Another 18 percent said they have "some" trust in Trump, while 22 percent said they have "a lot" of trust.

This isn't just a problem with Trump, though. When asked who they trust more to handle health care, 45 percent of voters said Democrats in Congress compared to 35 percent who said Republicans in Congress. And 53 percent said they have either "a lot" or "some" trust in Democrats on the issue, while 41 percent said the same for Republicans.

Trump began a new health-care push last week when it was announced that his Justice Department was asking courts to strike down all of ObamaCare. Trump subsequently said Republicans would try again to come up with a replacement for the health-care law, although he said on Monday that a vote on any replacement would be put off until 2021, all but ensuring health care will become a key issue in the 2020 presidential election.

Politico/Morning Consult's survey was conducted by speaking to 1,945 registered voters from March 29 - April 1. The margin of error is 2 percentage points. Read the full results at Politico. Brendan Morrow