A new Rasmussen Reports telephone survey in Texas shows the presidential race has grown slightly closer over the past month. John McCain now leads Barack Obama 48% to 39% in the Lone Star state.

Last month, McCain enjoyed a thirteen-point lead over the Democrat. In May, the Republican had just a five-point lead in the state. Nationally, since clinching the Democratic nomination, Obama has held onto a modest lead in the Rasmussen daily Presidential Tracking Poll.

McCain has a dominant 50% to 33% lead among men in Texas, but the two candidates are essentially tied among women.

The Republican draws support from 79% of voters in his own party, Obama is backed by 72% of Democrats and McCain leads 49% to 32% among unaffiliated voters. He led 56% to 30% among unaffiliateds in early June.

McCain is viewed favorably by 61% and unfavorably by 34%. Obama’s ratings are 50% favorably and 48% unfavorable.

A third of voters in Texas think Hillary Clinton should be Barack Obama’s running mate, while 45% disagree.

While just over a quarter (26%) of voters in Texas think McCain is too old to President, over half (53%) think Obama is too inexperienced.

Two-thirds of Texas voters (69%) favor drilling in offshore oil wells while 22% disagree. If offshore drilling were allowed, 59% of voters in Texas think it would be likely that gas prices would go down, while 34% find it unlikely.

Texas native President Bush earns good or excellent ratings from 41% of Texas voters, while 42% think the president is doing a poor job.

In the state’s U.S. Senate race, Republican incumbent John Cornyn leads Democratic challenger Rick Noriega by double-digits.

The survey was conducted in partnership with Fox Television Stations, Inc.

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