PITTSBURGH — Never has so much money been spent so quickly on a political race with so little real meaning than on the House special election here, but to Republicans, the public relations debacle that would come with a loss this Tuesday is a price they cannot bear.

Never mind that this southwest Pennsylvania seat — which envelops suburban Pittsburgh and hugs the West Virginia border — will most likely cease to exist by the November election or that the man occupying it will be shopping for new constituents. Conservative groups have flooded the district with more than $10 million. President Trump will be here on Saturday to test out the political potency of his new steel tariffs. Vice President Mike Pence has paid a visit.

And the Democrats are playing, too. On Tuesday, former Vice President Joseph R. Biden Jr. was at a union carpenters training center glad-handing supporters of Conor Lamb, the 33-year-old Democrat who hopes to pull off a huge upset next week in deepest Trump country.

“If he wins, you’re going to see probably another half a dozen Republicans say they’re not running again,” Mr. Biden told a reporter on a meet-and-greet rope line, adding that Mr. Lamb could also show the way toward that holiest of Democratic grails: “getting back working-class people supporting us again.”