Given a choice, 54% of rank-and-file Democrats and Democratic-leaning independents would prefer that their party move closer to the center
https://news.gallup.com/poll/245462/democrats-favor-moderate-party-gop-conservative.aspx
Among Democratic and Democratic-leaning registered voters, somewhat more say they want the Democratic Party to move in a more moderate (53%)
http://www.people-press.org/2019/01/24/publics-2019-priorities-economy-health-care-education-and-security-all-near-top-of-list/