WASHINGTON — Representative Jerrold Nadler of New York has a bold pitch to take over the top Democratic spot on the House Judiciary Committee — that he is best positioned to lead impeachment proceedings against President Trump.

“As our constitutional expert, and with his demonstrated leadership on impeachment in the 90s, Nadler is our strongest member to lead a potential impeachment,” Mr. Nadler wrote on a pocket-size leaflet outlining his record.

Not so fast, says Representative Zoe Lofgren of California, his main opponent for the slot. Not only was she on the committee when Bill Clinton was impeached in 1998, but she was a part of its staff during the proceedings against Richard M. Nixon two decades earlier — a better model, she argues, for taking on Mr. Trump.

Democrats have no shortage of priorities before the Judiciary Committee, which handles a range of hot-button issues, including immigration, guns, abortion and domestic surveillance. But with Democrats increasingly bullish about their chances of retaking the House next year, the candidates fighting for control of the committee have dispensed with niceties and are openly campaigning on the “I” word: Impeachment.