Mr. Lamb, who considers himself the winner despite talk of a recount, said on Wednesday that he would serve out the remainder of the term representing the voters in the current 18th district.

The contested seat was left open after Representative Tim Murphy, an anti-abortion Republican, was forced to resign when a former lover said he pressed her to have an abortion.

“It’s a special election and a very special experience,” Mr. Lamb told CNN on Wednesday. Mr. Lamb could take office in the next few weeks, shifting the breakdown in Congress to 238 Republicans, 194 Democrats and three vacant seats. Democrats would need to win 24 seats in November to take control of the House.

But the district Mr. Lamb will represent for the rest of the year will not be the district he runs for in the next Congress, the result of a court-ordered redistricting of the state’s congressional boundaries.

“We’ll let the rest of it shake out,” Mr. Lamb said. “There is a lot of work to be done just in trying to bring solutions to the problems we talked about in six months.”

The New Pennsylvania Congressional Map, District by District

Democrats couldn’t have asked for much more from the new map.

Next week starts the race for the November midterm elections

The uncertainty of the outcome of the special election has little bearing on the state’s primaries and general election, which effectively kick off on Tuesday — the deadline for candidates to file nominating petitions. In 2019, the 18th district that Mr. Lamb and Mr. Saccone are vying for will no longer exist in its current form, because of the state’s congressional redistricting.

Both men are likely to run in newly drawn districts, which means both Mr. Lamb and Mr. Saccone could find themselves as members of the Pennsylvania delegation in the 116th Congress.

Pennsylvania is a swing state that has backed politicians from both parties in the last two election cycles. Currently, Republicans control 13 of the 18 House seats. Experts think the newly drawn congressional districts will benefit Democrats.

Mr. Lamb is likely to run to be the Democratic candidate for the newly drawn 17th district, which includes more of the Pittsburgh suburbs and is favorable to Democrats.

That could be a crowded field for Democrats, according to Mr. Makhija, but he predicts Mr. Lamb will be a difficult candidate to beat in the primaries to be held on May 15.

Mr. Saccone is likely to run to be the Republican nominee in the new 14th district, which is heavily Republican. Mr. Makhija said the race for that seat has a fairly open field going into the Republican primaries. However, he said, “After last night, I don’t think there is such a thing as a safe Republican district.”

Even after the embarrassing defeat in the special Alabama Senate election three months ago, Mr. Trump threw his weight behind Mr. Saccone in what was considered friendly Republican territory. Mr. Trump campaigned twice with Mr. Saccone. The president mocked Mr. Lamb as “Lamb the sham,” a reference to Republicans’ contention that Mr. Lamb ran with a conservative agenda. Mr. Trump also gave a rambling, hour-plus speech in which he only mentioned Mr. Saccone a handful of times.

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