Back to the OP, I really don't think they wanted another outsider. Obama's win was an upset for the democrats, and he ultimately ended up being a disaster down-ballet. In his 8 years, they lost the senate, the house, the majority of governorships, and many state state legislatures. While he could do great during election years, he simply couldn't appeal to voters during midterms and at the state level, which really ruined the democrats ability to pass legislation.
I don't think Obama, or his presence, ever really resonated with voters after 2008. The Republican landslides in 2010 and 2014 speak for themselves, but it's seldom acknowledged that the popular vote in 2012 swung Republican by almost 3.5 points. Democrats had a MASSIVE advantage in the EC in 2012, which made Obama's win look more decisive than it was.