DALLAS — Vice President Mike Pence laid out a hopeful vision for the midterm elections this week as he campaigned for Representative Pete Sessions of Texas, telling Republican donors that candidates like Mr. Sessions could stop Democrats from winning the House in November.

“The road, they know, to their majority comes right through Pete’s district,” Mr. Pence said. Referring to this city’s vote-rich suburbs of undecided moderates, he added, “Make sure the red wave starts here.”

Mr. Pence was deploying a favorite image of both Republicans and Democrats this fall: An electoral tidal wave of voters carrying their party to power in Congress. But the point of his trip was not to stir a wave. It was to build a wall.

As they brace for losses in the House of Representatives, Republican Party leaders are racing to reinforce their candidates in about two-dozen districts, trying to create a barricade around their imperiled majority. They are pouring money and effort mainly into moderate suburban areas, like Mr. Sessions’s seat, that they see as critical to holding the chamber by even a one-seat margin. And they have begun to pull millions of dollars away from Republican candidates who have fallen substantially behind in once-competitive races.