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Ms. Duffy said the tea party’s first true test of 2012 likely will be in Texas, where Mr. Cruz, a former state solicitor general who has argued nine cases before the Supreme Court, is set to face off in a March 6 primary election against Lt. Gov. David Dewhurst, the favorite, and others.

But she said that there is not a ton of evidence that Mr. Cruz has caught fire in the state, where it costs a candidate major money to raise his name ID and get his message out over the airwaves.

“Texas is — unlike certainly Kentucky, and to a lesser extent Florida — an inefficient state in terms of TV,” Ms. Duffy said, estimating the cost of running television advertisements across the sprawling state’s 15 to 20 major TV markets at between $1.5 million and $2 million per week.

“It is a hard place to get yourself known,” she said.

Mr. Cruz, though, is confident he can raise the money necessary to increase his name ID and win — thanks in large part to local and national tea party support. Freedomworks, led by former House Majority Leader Dick Armey of Texas, and the Club for Growth endorsed him. He also has won the backing of such out-of-state tea party favorites as Sen. Patrick J. Toomey of Pennsylvania, Mr. DeMint, Mr. Paul and Mr. Lee.

Conservative columnist George Will wrote this summer that Mr. Cruz is “as good as it gets” for a political candidate and relayed the story of how Mr. Cruz’s father fought with rebels against 1950s Cuban dictator Fulgencio Batista before he was captured and escaped to the United States with $100 sewed into his underwear.

Mr. Cruz said his campaign is “building the strongest grass-roots army the state of Texas has ever seen.”

“We have an overwhelming advantage among tea party members, among women, among conservative leaders, and that army on the ground consists of the activists who knock on doors, who send emails and who talk to friends and family and who win a Republican primary,” he said.