Tuesday’s special runoff election for Texas’s 6th Congressional District has been billed as the first test showing former president Donald Trump’s influence within the Republican Party. It could prove just the opposite.

The race is between two Republicans for a seat south of Dallas and Fort Worth that became vacant because of the untimely death of its incumbent, Rep. Ron Wright (R), of covid-19. His widow, Susan Wright, picked up the most votes in the special election on May 1 after receiving Trump’s late endorsement. The fact that she did much better after Trump’s blessing than she did in early voting was touted as evidence that his word still carried weight.

That weight wasn’t all that heavy, however, as she received only 19 percent of the vote. More tellingly, she received about 31 percent of all votes cast for Republicans. That’s not a strong showing, considering that, in addition to Trump’s backing, she had some residual name identification from being the former incumbent’s widow. Her poor fundraising — she raised a paltry $740,000 for the whole election as of July 7 — also indicates weakness.

These factors give her GOP opponent, state Rep. Jake Ellzey, some hope of pulling off an upset. He finished second with 13.8 percent of the total vote and has a base of support in his home county, Ellis. He raised $1.7 million for the whole cycle, allowing him to vastly outspend Wright, especially in digital advertising. The conservative Club for Growth has run ads on Wright’s behalf, with a new one attacking Ellzey for allegedly missing votes as a state representative and supporting a tax hike. Trump’s PAC is also spending on last-minute television ads for Wright, and Trump will reportedly hold a tele-rally Monday night for her.

So far, however, all of this effort has not produced much interest. Only 20,534 people had cast ballots by Friday, when early voting ended. This abysmally low turnout follows low voting levels in the first round, when about 78,000 people voted, including more than 45,000 early ballots. Last November, the district attracted more than 344,000 votes. Wright’s own pollster stated that a low turnout favors its candidate, but it’s still telling that a Trump endorsement isn’t generating much interest in the race.

Widows tend to do well when running to succeed their late husbands. At least 47 women in history have won election to the House or Senate following their spouse’s passing. That doesn’t include Rep. Julia Letlow (R-La.), who won a March race to succeed her late husband, Luke Letlow, who won election last year but died of covid-19 before he could take office. That factor complicates an assessment of Trump’s impact on the outcome, although Wright’s weak fundraising suggests she might not have the strength other widows have displayed.

Ellzey’s hope rests on winning Ellis County by a large margin and losing the most populous county in the district, Tarrant, by 10 points or less. On election night, watch the early returns: If Ellzey breaks 62 percent in Ellis and 45 percent in Tarrant, he has a shot. Anything less, and Wright will probably win.

Those assessing Trump’s influence, however, should look more to the turnout than to the result. If Wright wins but turnout remains extremely low, that suggests — at best — that Trump’s word is influential among a small but devoted band of base voters. That’s not unimportant, but it’s far from the deep influence many observers think he has. Far from being able to make or break careers with his gaze, it’s possible that all Trump can do is motivate a small percentage of the Republican base to do his bidding. If that’s true, anyone with conservative views and a base of support can stand against him and win.

No single race can fully assess a national trend. Local factors always matter in intraparty primaries, and the timing of this election for early August always augured a lower than normal turnout. Tuesday’s outcome will nonetheless be parsed for its greater meaning. Anything less than a big Wright win with a larger than expected turnout suggests Trump isn’t as strong as many think.