The argument they would make usually went something along the lines that voting should involve effort and inconvenience and sacrifice, because it’s such an important part of being a citizen and visibly showing your commitment to the community. It was truly boneheaded Protestant work ethic stuff, steeped in privilege, from people who (unlike conservatives) should have known better.
I haven’t heard that argument from on Internet forums (at least not from liberals) in about a decade, but I have no doubt that older Dems are still out there who believe that nonsense.
To be clear, I don’t have any problem with people who like voting on election day. They just shouldn’t limit everyone else’s options.