Darren Hodges, a Tea Party Republican and councilman in the windy West Texas city of Fort Stockton, is a fierce defender of his town’s decision to ban plastic bags. It was a local solution to a local problem and one, he says, city officials had a “God-given right” to make.

But the power of Fort Stockton and other cities to govern themselves is under attack in the state capital, Austin. The new Republican governor, Greg Abbott, has warned that several cities are undermining the business-friendly “Texas model” with a patchwork of ill-conceived regulations. Conservative legislators, already angered by a ban on fracking that was enacted by popular vote in the town of Denton last fall, quickly followed up with a host of bills to curtail local power.

“The truth is, Texas is being California-ized, and you may not even be noticing it,” Mr. Abbott said in a speech at the Texas Public Policy Foundation, an influential conservative think tank, just before he took office last month. “Large cities that represent about 75 percent of the population in this state are doing this to us. Unchecked overregulation by cities will turn the Texas miracle into the California nightmare.”

His salvo caught Texas cities by surprise. But pre-empting the power of local governments is becoming a standard part of the legislative playbook in many states where Republicans who control statehouses are looking to block or overturn the actions of leaders, and even voters, in municipalities that are often more liberal.