The relationship between Democratic elected officials and the Democratic Party is complex. Usually the Party, local, state, or national, is controlled by the most powerful elected official at that level, although that isn't always the case. The Democratic Party of Dane County, for instance, is essentially controlled, quietly and behind the scenes, by a union, AFSCME Council 40.
But I digress. The question is if unpopular policy positions taken by Democratic elected officials can significantly damage the Democratic Party. The answer is clearly yes. Back in the mid 1960's the Democratic Party of Wisconsin lost more than two-thirds of its members because of Lyndon Johnson's support for the Vietnam War, dropping from 27,000 in 1964 to 8,000 in 1967. Even today, after more than forty years, the DPW has never come close to its former size, with current membership hovering a little under 10,000. There are many reasons for that, but one is a divisive war fought a generation ago.