I'd say "Democrat-led" is fine, just as "programmer-led" would be fine. "I am a Democrat"/"I am a programmer"; "I am in the Democratic party"/"I am in a program

I'd say "Democrat-led" is fine, just as "programmer-led" would be fine. "I am a Democrat"/"I am a programmer"; "I am in the Democratic party"/"I am in a programmers' union".