Republican Party voters in the U.S. state of Texas may hand the party's staunchly conservative Tea Party movement another victory when they cast ballots in Tuesday's runoff vote in a U.S. Senate primary race.

Longtime Lieutenant Governor David Dewhurst easily won the first round of the primary in June, but failed to win the majority needed to avoid a runoff against first-time candidate Ted Cruz, a former state solicitor general . Dewhurst, who enjoyed support from Governor Rick Perry and other leading Republican figures, was believed to be the overwhelming favorite to win the runoff.

But Cruz has energized his fellow Tea Party members across the state in recent weeks, with help from Sarah Palin, the former Alaska governor and vice-presidential candidate who is widely popular within the movement.

Recent voter opinion polls show the race to be extremely close, with one poll showing Cruz with a substantial lead heading into Tuesday's vote. The winner would be the overwhelming favorite to replace retiring Senator Kay Bailey Hutchinson, since no Democrat has been elected to a statewide seat in Texas since 1994.

A victory by Cruz, who would be the first Hispanic U.S. senator from Texas, would be further proof that the Tea Party movement, which demands low taxes and deep cuts in government spending, has emerged as a powerful force within the Republican Party. Earlier this year in the state of Indian, a Tea Party-backed candidate, Richard Mourdock, defeated veteran Senator Richard Lugar in a primary election.