The Lyceum Poll from the University of Texas asks voters every year what they think about a variety of public policy issues.
This year, the poll wanted to know voters' opinions on using Medicaid to cover more Texans.
Governor Rick Perry has repeatedly said "no" to Medicaid expansion under the Affordable Care Act — even though the federal government would pick up all the extra cost for three years — and most of the cost after that.
Poll director Daron Shaw says voters were asked whether they favored Medicaid expansion — even when confronted with arguments that it would cost too much, or that the program is not effective.
"What we found, basically, is that 50 percent said we should take the money and participate in this Medicaid expansion. Forty percent said, no, we shouldn't — that's not what we ought to be doing right now."
Shaw says he would have predicted the opposite — with a majority against expanding Medicaid.
"Because of the public conversation in the state over the last few years, that Texans would oppose participation in a program where the federal government is kinda promoting it."
Shaw says Democrats may use the results during the next legislative session to try to persuade the Governor to accept federal money for Medicaid expansion.