According to the latest University of Texas/Texas Tribune Poll, 39% of Texans somewhat support or strongly support Abbot's move to send the State Guard to monitor the military's Jade Helm 15 exercises in Central Texas.
The war games are being held across multiple southwestern states where the terrain is similar to that which troops will face in other parts of the world.
On the other side, 28% either somewhat or strongly oppose sending the state guard to monitor the military, while 32% did not know or had no opinion of the governor's action.
Abbot deployed the Guard after alarmed Texans claimed that the military was being used to impose martial law and that recently closed Walmart stores were being used to help take over areas.
Of all the groups surveyed, the poll found support for Abbott's actions were the highest (85%) among Tea Party Republicans.
"This is an action that played to a very specific audience," Jim Henson, head of the Texas Politics Project at the University of Texas at Austin and co-director of the poll, told the Texas Tribune.
"Despite the criticism that Gov. Abbott took from the national press and from his political opponents," Henson said, "he was pretty much in the comfort zone of his political base, in both taking this action and in the way that he took it. There's no evidence here that he should expect any backlash in Texas."
A majority said federal military intervention is "very" or "somewhat" likely to arrest political protesters, and 50% said it is likely that the feds would send the military to violate citizens' property rights. Smaller but significant numbers said the military would likely be used to impose martial law (44%) and to confiscate firearms from citizens (43%).
"You put federal government into it and people's skepticism and their concern really rises," Daron Shaw, co-director of the poll and a professor of government at UT-Austin, was quoted as saying by the Texas Tribune.
And while Republicans are more wary than Democrats are of the federal government, the sense of suspicion is present in both parties.
"Nobody trusts the federal government" Shaw said. "About a third of Democrats are concerned about the government going nuts. Among Republicans, it's between 55 percent and two-thirds."