She is barely a blip in the polls, and the odds of her securing the Republican nomination for Texas governor are viewed as vanishingly small. But Lisa Fritsch, a conservative activist, author and former radio show host, suddenly has bragging rights among second-tier candidates trying to make a respectable showing against the primary favorite, Attorney General Greg Abbott.

In a recent poll, Ms. Fritsch came out ahead — just barely — of the former Texas Republican Party chairman Tom Pauken, once an appointee of Gov. Rick Perry on the Texas Workforce Commission. She was also the top Republican vote getter in a Tea Party straw poll in Austin last weekend, although Kathie Glass, a Libertarian, won the poll, with 48 percent. Ms. Fritsch was second at 27 percent, and Mr. Pauken had 21 percent.

Mr. Abbott, a no-show at the New Revolution Now Tea Party forum, had 4 percent.

Ms. Fritsch, 38, who said she had faced long odds all her life, took inspiration from Texas history to size up the battle ahead.

“What if Davy Crockett had said, ‘How could we compete with the Mexican Army at the Alamo?’ ” she said. “Should they have given up? Absolutely not.”