Democratic senator says party must accept reality and 'change' after Trump win

"There'll be plenty of opportunities for us to fight on matters of real principle, where our argument is that that's going to make life harder and more expensive for people," Welch told the outlet. "But not just because we don't like Trump."

Some Democrats, like Colorado Sen. John Hickenlooper, are signaling that they are able to find some points of agreement with Republicans in order to advance policy goals. 

"Within that, there's a million things that need to be decided. So I'd be happy to try and find compromises wherever possible," Hickenlooper told Semafor. 

"On a given day, I'm doing both things: Trying to get things passed, and also trying to stop bad things from happening," Kaine said of how his job has changed following the ascension of Republicans to the Senate and other halls of power.

Fox News' Gabriel Hays contributed to this report.