AUSTIN, Tex.  President Obama shared an enthusiastic handshake and a hearty clap on the shoulder with this state’s Republican governor, Rick Perry, when Air Force One touched down here on Monday.

But while Mr. Perry, who is running for re-election, stood on the tarmac and clapped for the president, his Democratic challenger, Bill White, was nowhere to be seen.

The decision by Mr. White, a former mayor of Houston, to avoid the visit of a sitting president from his own party needed little explanation: as a moderate Democrat in a state controlled by Republicans, he could ill afford to cozy up to Mr. Obama, who is being characterized as a tax-and-spend liberal by some of Texas’ more conservative politicians, and by Mr. White himself.

The disappearing act by Mr. White, who said he would be on the campaign trail elsewhere in the state, points up a conundrum for Mr. Obama in this midterm election season. While the president remains a powerful fund-raiser for the Democratic Party  he brought in more than $1.6 million on Monday during back-to-back events in Austin and Dallas  his travels do not always sit well with the candidates whose campaigns he is hoping to help.