That's a very complex question and if I am not careful in answering I will only cause confusion. The term "Leftists" has many meanings to me. I consider moral liberality to be more leftist than fiscal liberality and there are large groups of both in the Democratic party. I know there are actually Democrats that seem to want to become communist. This should be no surprise since we live in a country with people that want to catch aids "bug chasers".
But those are extremes.
We are already very very socialistic in this country. Socializing all medical care may be a next goal on the socialistic agenda and it would certainly be the Democrats that are more likely to push that. So yes I guess I have to agree with you.