DALLAS (CBSDFW.COM) –  One week from today, Texans will go to the polls for the state primary.

Republican presidential candidate Mitt Romney will likely win enough delegates in Texas to officially become the nominee.

But the race with the biggest political stakes is the Republican primary for the open U.S. Senate seat.

It’s being vacated by Kay Bailey Hutchison, who is retiring.

Lt. Governor David Dewhurst is in a real fight against former state Solicitor General Ted Cruz.

Cruz believes “This race is in single digits. We are headed to a run-off.”

Dewhurst says, “This isn’t a nine point race.”

Political analysts say the main storyline is whether Dewhurst, an establishment conservative, can hold back Cruz, a Tea Party favorite.

Former Alaska Governor and vice-presidential candidate Sarah Palin backs Cruz.

Governor Rick Perry supports Dewhurst.

And the candidates’ supporters have spent millions of dollars on negative television ads bashing their opponents.

Cruz says, “Two days after Sarah Palin endorsed me in this race, they doubled their ad buys so they’re now spending $2 million dollars a week in negative, false attack ads directed at me.”

Dewhurst says, “There isn’t one charge the Washington insiders or Mr. Cruz has made that is true. I’m forced to be in a situation where I have to defend myself.”

Former Dallas Mayor Tom Leppert believes he still has a shot to be in a runoff with Dewhurst — but acknowledges he has to run strongly here in North Texas.

Leppert says, “We’ve had our strategy and that’s played out as we wanted it to. We’ve got a lot of momentum, we’ve seen the numbers, and we feel very good about this.”

Former football player and ESPN broadcaster Craig James says he shouldn’t be counted out despite his low position in the polls.  James says, “The message has resonated and I know the grass roots folks who’ve converted to me are real, so that kind of polling I’m very confident in.”

But political analyst John Weekley believes the race will come down to Dewhurst and Cruz.  He says, “If the election were held today, I think there very probably is going to be a runoff.  So far, Cruz has stayed in the 30% range, Dewhurst has stayed basically in the 40% range.”

If there is a run-off between Dewhurst and Cruz, it will be a real test for the Tea Party here in Texas. And analysts believe a run-off will re-set the entire race.

The runoff would be held on Tuesday, July 31.

Four people are running for the Democratic nomination.