The group includes moderates and senators known for crossing party lines, a few who are retiring and some who had already broken with their party to support same-sex marriage.
They may still win the House. But an underwhelming showing has the G.O.P. wrestling with what went wrong: Was it bad candidates, a bad message or Donald J. Trump?
Senator Mike Lee, in a surprisingly close race for re-election, has antagonized Mitt Romney and the state’s G.O.P. for years. His plea now? “Please, get on board.”