Flanked by lawmakers at the State Capitol, Mr. Abbott, a staunch Republican who has found himself defending his conservative credentials in recent months, said the state was “stepping up to get the job done.” But his announcement was dismissed by critics and immigration advocates as political theater and an obvious attempt to appease right-leaning voters ahead of his re-election bid next year. “If the governor wants to blow hot air on TV, he can do that,” said David Donatti, a staff attorney for the American Civil Liberties Union of Texas. “I truly don’t think he has thought this through. The governor is not a king. We have checks and balances in the state of Texas.” Still, Mr. Abbott cast aside the derision in his push to finance construction of a barrier along the border. He said he would set aside $250 million from the state’s general revenue as a down payment and hire a program manager who would determine the total cost of the project and the length of the wall. But he was short on other details, saying they would emerge later.