By Matt Goodman,

FORT WORTH (CBSDFW.COM) – Lt. Gov. David Dewhurst did not win enough votes Tuesday to secure the GOP nomination for the vacant U.S. Senate seat without a runoff against tea party-backed Ted Cruz. Nor did Democratic leader Paul Sadler, who will face Grady Yarbrough, a San Antonio challenger who doesn’t have a campaign website.

Dewhurst will face former Texas Solicitor General Cruz, who won about 34 percent of the vote compared to Dewhurst’s 45 percent.

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Speaking at her husband’s campaign party in Houston, Tricia Dewhurst said she was “hoping to avoid a runoff, but (is) energized either way.” She said she is “inspired by David’s energy and enthusiasm.”

Former Dallas Mayor Tom Leppert threw in the towel after falling behind early at about 7:30 p.m. with only 8 percent of precincts reporting. Leppert finished with 13 percent of the vote.

Sports broadcaster Craig James managed to secure just 4 percent of the vote.

After the runoff was declared, Dewhurst spoke to his supporters in Houston, saying he aimed to “stop the out of control spending from Washington” and “balance the budget just like we do here in Texas without raising taxes.”

“Tonight, we Republicans sent a message to President Obama: Stop the war on Texas,” Dewhurst said to a cheering room. “And that’s exactly what I’ll help to do as your next United States Senator.”

When Cruz took the stage moments later at his own celebratory event in Houston, he greeted supporters with, “Wow. We did it.”

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“A year and a half ago there wasn’t a soul in the state of Texas that thought this was possible,” Cruz said, prompting one supporter to yell otherwise. “But I’ll tell you, tonight was a victory for conservatives.”

The runoff was reported with 38 percent of precincts reporting.

The Democratic race for that same seat also ended with a runoff. Paul Sadler, an attorney who served in the state House from 1991 to 2003, ensured his presence.

The race between his competitors was too close to call until about 10:40 p.m. Grady Yarbrough, of San Antonio, had 26 percent of the vote while his opponent Addie Allen had 23 percent with 89 percent of precincts reporting.

Allen lives in Beaumont and has a long history as a city employee. The Associated Press described Yarbrough as a “political unknown” who “has run as a Democrat and a Republican in previous elections.”

Republican U.S. Senator Kay Bailey Hutchison is retiring. She’s served as the state’s senior Senator since 1993.

Texas has not elected a Democratic candidate to that Senate seat since 1988.

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CBS 11’s Jack Fink contributed to this report.