In what sense is the (radical right) ruling faction of the Republican party "conservative"? There is a case to be made for genuine conservatives as stabilizers of traditional social orders that have evolved features that no one fully understands. There is little that can be said for radicals who favor overturning law and a liberal social order in favor of greed, war, and authoritarian rule.
Today, Democrats are indeed conservative: The US tradition they are defending includes relatively strong support for rule of law, personal liberty, social welfare, and so on. Democrats are fighting to reverse recent erosion of these traditions. Surely this noble effort is conservative, perhaps even reactionary. Words and ideas I offer here may be used freely and without attribution.