A top House Energy and Commerce Republican is reaching across the aisle on legislation to resurrect plans for storing nuclear waste at Nevada’s Yucca Mountain.

But Nevadans who have long opposed the project say they’re in a better political position now that the Democrats control the House.

Rep. John Shimkus (R-Ill.), the ranking member of the House Energy and Commerce environment subcommittee, said he is working with Democrats to revive a version of his bill that passed the House last Congress but was never taken up in the Senate.

“You don’t find very many bills that get 340 [yes]...