By Corrie MacLaggan

AUSTIN, Texas (Reuters) - A U.S. Senate candidate in Texas with Tea Party backing may win enough votes in Tuesday's Republican primary to force a runoff with the state's lieutenant governor, setting up another battle for the soul of the national Republican Party.

Twice this year an insurgent conservative Senate candidate has upended a traditional Republican - in Indiana, where a candidate backed by the Tea Party movement beat longtime U.S. Senator Richard Lugar, and in Nebraska, where first-time statewide candidate Deb Fischer defeated a veteran attorney general.

Emboldened by the victories, national conservatives have turned their attention to Texas, where they believe Cuban-American Ted Cruz could be a new Republican star.

Last year, it seemed unlikely that the Texas front-runner, Lieutenant Governor David Dewhurst, would face a serious threat for the seat that Republican Senator Kay Bailey Hutchison is leaving after 19 years on the job.

But that was before former state Solicitor General Cruz started drawing money from national conservative groups such as Club for Growth and FreedomWorks, and endorsements from former vice presidential nominee Sarah Palin and former presidential candidate Rick Santorum.

Dewhurst, who has the backing of Texas Governor Rick Perry, is now locked in a battle with Cruz, a Houston lawyer whose father came from Cuba with $100 sewn into his underwear.

The Republican race - almost certainly the only primary that matters in a state that has not elected a Democrat to statewide office since 1994 - is shaping up as a fight over who is the most conservative.

It looks unlikely that Dewhurst will be able to win the 50 percent-plus-one votes necessary to avoid a runoff on July 31 between the top two candidates, said Mark Jones, chairman of the political science department at Rice University in Houston.

"Everything started snowballing," Jones said. "The Cruz campaign keeps generating more and more enthusiasm."

A University of Texas/Texas Tribune poll released on Monday showed Dewhurst had the support of 40 percent of likely Republican primary voters, and Cruz had 31 percent. Former Dallas Mayor Tom Leppert had 17 percent and Craig James, a former NFL football player and ESPN analyst, got 4 percent. Another poll has Dewhurst at 46 percent, closer to the magic number to avoid a runoff.

NATIONAL ATTENTION

Dewhurst has loaned his campaign $9.2 million, his campaign said. Cruz has received $3.6 million from the Club for Growth since last December, according to regulatory filings and recent statements from the group. The Senate Conservatives Fund, led by Jim DeMint, a Republican U.S. senator from South Carolina beloved by the Tea Party, has spent just over $1 million for Cruz.

FreedomWorks has hosted 26 grassroots training events in the past year in Texas, where it has 32 distribution centers that provide volunteers with Ted Cruz yard signs and door hangers, according to Brendan Steinhauser, its director of campaigns.

The Tea Party movement and its backers, who are seeking deep cuts in U.S. government spending, say they want to elect "true" conservative candidates - such as the upstarts in Indiana and Nebraska - who will challenge the status quo in Washington. Continued...