Even though George Bush won the state in 2004 with 61 percent of the vote, Texans are not as enthusiastic at the moment about John McCain. He has a single digit lead over Barack Obama, 43-38. Seventeen percent are undecided.
And even more - 24 percent - are undecided about the Senate race. Incumbent Republican John Cornyn has a very narrow edge over Democratic challenger Rick Noriega, 38-34 percent. CQ Politics rates the race as Republican Favored.
The telephone survey was conducted June 12-20 and respondents could answer in English or Spanish. The margin of error was +/- 3.1 percentage points.
Meanwhile, in a Rasmussen poll, McCain led Obama by a larger margin: 48-39, though Rasmussen said that is a smaller margin than last month, which was 13 points.
And, Rasmussen also had a much larger difference than Lyceum for the Cornyn-Noriega race: 48-35 percent. That, too, was down from last month's results: 52-35.
The Rasmussen poll has a margin of error of +/- 4.5 percentage points.