President Donald Trump will have to either resubmit nominees or make new selections for nearly a dozen positions at the EPA and the Energy and Interior departments in 2019, barring increasingly unlikely Senate action in the days ahead.

Without a last-minute deal, Trump will have decide what to do about a pile of nominees—some of whom have drawn sharp criticism from Democrats—that never got floor consideration in the 115th Congress. In the new Congress starting Jan 3, Trump will have...