They simply need to solve their problem. That they have it is absurd and makes them look pathetic, cowed, and ineffectual victims - not something people vote for. What is more important to a political party than a means of public communication?
Democrats are making many statements. If they are not "major", it is perhaps because nobody cares about statements. They care about the exercise of power, and Democrats have none. Any statement they make is easily dismissed as bluster.
The first sentence is true, the second absolutely false. Public, political communication is all about that second issue - look how effective the GOP is. They can make absolute nonsense into a norm; they can shut down any speech they don't want.
Name a major Democrat. There is none. After 3 electoral cycles when party bureaucracy each time crowned the candidate instead of a candidate rising through the primaries the party has no leaders anymore - note the difference between a leader and a top bureaucrat, the Dems have no deficit of the latter.
However, I was referring to the lack of a mechanism. Whatever the Dems say, almost nobody hears it. Name a major statement by a Democrat in the last week? In the last month?