Come Wednesday morning, at least one pollster will have some explaining to do about final numbers heading into Tuesday’s Texas Senate runoff.  That’s because the last surveys released over the weekend showed both Lt. Gov. David Dewhurst and former Texas Solicitor General Ted Cruz ahead.

A Dewhurst poll conducted last week showed him ahead of Cruz by 5 points. Then Public Policy Polling, a Democratic polling firm, released an automated survey that showed Cruz up by 10 points.

Cruz has steadily built momentum since the late May primary, and most observers of the race believe he will win — probably by a comfortable margin. Sources in the Cruz camp were confident going into the weekend, saying their polling has held steady since Roll Call obtained a late June internal survey that showed Cruz in the lead.

The Dewhurst poll was conducted among 1,106 “likely Republican primary voters” and had a margin of error of 2.9 points. In that survey, Dewhurst got 48 percent to 43 percent for Cruz.

“Our poll is more inclusive in that it casts a slightly wider net, and rightfully so,” Dewhurst pollster Mike Baselice wrote in a memo released to the press Sunday.

The Cruz team has not released a recent poll, but sources said polling by WPA Opinion Research gives the team confidence in the final stretch. Their polling samples over the last month have included only GOP voters who went to the polls for the May 29 primary.

The Dewhurst camp has strongly contested that methodology. A Dewhurst source raised questions during the weekend about the Cruz poll, countering that 16 percent of voters who have cast ballots in the runoff did not vote May 29.

PPP screened those who had voted “in any Republican primary election in the last 10 years” and included people who “said either that they had already voted or that they were definitely going to vote,” according to PPP Director Tom Jensen. The PPP survey was conducted July 28-29 and had a margin of error of 3.8 points.

In a late May survey of the GOP primary electorate, a PPP poll showed Dewhurst polling at 46 percent and Cruz at 29 percent. In the final election results, Dewhurst got 45 percent of the vote and Cruz got 34 percent.

Beyond polling, Dewhurst infused his campaign with an additional $8 million from his own pocket in the past month. Part of that money, and the money of outside groups supporting Cruz, such as the Club for Growth, has gone toward a pervasive television ad campaign during the Olympics over the weekend.

Several Texas political watchers have said the Dewhurst television ads have saturated the air for so many months that they are losing their effectiveness. They also take care to note that the negative ads are especially wearing thin.

But there is more to this race than extravagant television spending and high-profile endorsers swamping the state to get-out-the-vote. Dewhurst has made a strategic direct-mail effort to target senior citizens, who can vote via mail-in ballot.

A Dewhurst source noted Sunday that 66 percent of early voting and mail-in ballots have come from voters older than 60.

Part of the mail-in ballot strategy is to work around the triple-digit heat hitting Texas this week. It is expected to be hot in Texas on Tuesday — 106 degrees in Dallas, 102 degrees in Austin, 101 degrees in Lubbock, 103 degrees in San Antonio, 97 degrees in El Paso and a breezy 95 degrees in Houston.

That heat, especially in the more humid areas of the state, has the potential to be as stifling as icy weather in winter primaries in northern regions of the country.

Elsewhere, Cruz has made an effort both in the primary and the runoff to target areas where there are downballot runoff races in hopes of a reverse coattails effect.

Roll Call rates this race as Safe Republican. Whichever candidate wins Tuesday night will be heavily favored to replace retiring Sen. Kay Bailey Hutchison (R).