WASHINGTON — Back in May, Rep. Hakeem Jeffries, D-N.Y., the minority leader, saw a crucial piece of his strategy for winning control of the House slipping away.

Republicans, spurred on by President Donald Trump, had redrawn congressional districts in Florida to favor themselves, and Rep. Jared Moskowitz, a centrist Democrat from Coral Springs, was thinking of quitting rather than fighting for a third term in a far more conservative district.

Death threats were already jamming up his voicemail, and Moskowitz was frightened of what would happen to his family as Republicans trained their attacks on him.

Jeffries would not hear of it. In calls and meetings, he leaned hard on Moskowitz to stay in the race, telling him he was the key to a play to hold on to all four Democratic districts that Republicans in the state had carved up to protect the GOP majority.

“You’re the only one who can win that seat,” Jeffries told him, promising to match the torrent of Republican money that would be spent against him.…