If Mr. Lamb, a Marine veteran and a former federal prosecutor, defeats State Representative Rick Saccone, a Republican, in a district that the president carried by 20 points, the alarm bells will be audible across the country. The Democrats will have shown that they can breach the Republican hold on the blue-collar white voters who helped deliver Mr. Trump the presidency.
“If the Democrats were to prevail in western Pennsylvania, that would be quite an earthquake, let’s face it,” said Representative Charlie Dent, a Republican who represents a district in the eastern part of the state. “If a strong pro-Trump district like this goes the other way, it would send a bad signal around the country in districts far more competitive than this one.”
What is so remarkable about the Republican intervention is the ephemeral impact of its outcome. The lawmaker who held the seat — a married man and an opponent of abortion — fled Congress after his mistress let it be known that he had pressed her to have an abortion. Since then, the State Supreme Court has redrawn Pennsylvania’s congressional lines, and Mr. Lamb will live in another district come November.
Win or lose, he will probably be running against another Republican lawmaker in a more Democrat-friendly district slightly to the north.
Yet Republican officials, who believe that Mr. Saccone is a pedestrian candidate, say they could not simply abandon such a red-tinted region, especially with the White House unveiling tariffs aimed at bolstering the steel industry and eager to keep its grip on the crucial industrial Midwest this year and in 2020.
Now, with Mr. Lamb gaining ground, they are doing everything they can to push Mr. Saccone over the finish line, including a bit of political gamesmanship. The Congressional Leadership Fund, the leading House Republican “super PAC,” is sending mail to Democratic households depicting Mr. Lamb firing an assault rifle and noting that he supports gun rights — part of an attempt to dilute his support among more liberal voters.
The group has also put together a deceptive digital ad made to look like a cable television news report that portrays Mr. Lamb as reaching a “boiling point” with the labor unions, a pillar of his support.
“Democrat abandons PA Unions,” the ad says, noting that he opposes raising the minimum wage to $15 an hour. While Mr. Lamb does oppose such an increase, he enjoys overwhelming support from unions.
In an interview, Mr. Lamb said that he was running in part because he was “upset we weren’t competing everywhere,” and he argued that his success, in the wake of the West Virginia teachers’ strike, could help reinvigorate the beleaguered union movement.
“It could send a message that we have rebuilt and reconnected our link with organized labor,” he said. “They’re at the top of our agenda.”
This appeal, along with Mr. Lamb’s unapologetic opposition to Representative Nancy Pelosi, the House Democratic leader, has offered other Rust Belt Democrats something of a model for how to run in the Trump era.
If that gives Ms. Pelosi, who is eyeing a return to the speakership, pause, it troubles Mr. Trump and his allies even more as they aim to hold together their 2016 coalition. The president will have visited the district twice by Tuesday, and other administration officials have come for their own events.
Ronna McDaniel, the Republican National Committee chairwoman, noted that Mr. Lamb is “running like a Republican,” pointing out not just his opposition to gun control but also his support for the president’s tariffs.
But Ms. McDaniel said that the overarching reason the party and the White House are competing so aggressively is they know Democrats are energized and history suggests they could make big gains this fall.
“Every seat is going to count when you have a 24-seat majority,” she said.
The R.N.C., which in the past rarely got involved in House races, has spent more than $900,000 here.
It is this worry about just how high the Democratic wave could crest in November and the momentum they could pick up here that has prompted so much spending by Republicans.
While Mr. Lamb had raised nearly $4 million as of Feb. 21, much of it online from out-of-state progressives eager to win anywhere they can, Mr. Saccone’s campaign has been largely underwritten by outside groups. While Republican-aligned groups spent $9.7 million as of late February, Democratic groups had put in only $849,000.
The House Republican super PAC has not only unleashed a barrage of commercials and mailers, but it has also funded canvassers, a small group of whom were making their way through a middle-class subdivision just west of Pittsburgh the morning after Mr. Biden was in town.
Armed with an app that displayed the precise voting history and partisan tendencies of each household, the door-knockers found few residents at home for a piece of literature that deemed Mr. Lamb a “Rubber Stamp for Nancy Pelosi,” as well as a throwback “Stop Hillary” warning.
But those Republicans who did come to the door were receptive to Mr. Saccone and aware of the election.
“We’re voting for Rick,” Derek Soose interjected before a canvasser could complete his sentence.
Back in Washington, it is not difficult to find Republicans frustrated by all the money being dumped in a soon-to-be-redrawn district.
Some party strategists complain that the spending will seem misguided come October should Republican lawmakers find themselves in unexpectedly difficult elections and require money that may not be available.
Notably, the U.S. Chamber of Commerce, one of the most influential Republican-aligned groups, decided to stay out of the district after meeting with Mr. Saccone.
“We made a strategic decision to take a pass and focus on selling tax reform and linking it to pro-growth candidates that can win,” said Scott Reed, the chamber’s top strategist.
But former Representative Thomas M. Davis III, a Virginia Republican who once ran the House campaign arm, said Mr. Lamb may prove more vulnerable should he win on Tuesday, because he would have a voting record for conservatives to use against him in the fall.
In any event, Mr. Davis bluntly suggested that there was a bigger reason Republicans were so desperate to prevent disaster in Pennsylvania: They must spend money to keep raising money.
“A lot of transactional money in Washington will start moving when they see results,” Mr. Davis said, referring to the lobbyists whose contribution decisions are guided in part by which party they believe will wield power next year. “Like in the stock market, you want to stay on winning side.”
Democrats agree that the results will resound beyond this corner of Pennsylvania.
Reminded that Mr. Lamb was competing in an ancestral coal and steel district, the sort of place that has been firmly in the grip of Mr. Trump, Mr. Biden grinned and shot back: “Tell you what, it ain’t going to be anymore.”