My understanding is that the Democrats want to leverage a strong federal government to various aims (welfare, social security, medicare, medicaid, regulation, etc) while the Republicans want a smaller federal government and give the power to the states. This divide is about power of the federal government vs power of the states, or the Jeffersonian / Hamiltonian divide.

You've shown examples of where the Democrats want more direct democracy, so there's that too. I don't know if this is a recent phenomenon or not. I've never known the Ds to make much about it either way until you mentioned it.