You are looking at the end results only, not the goals, the efforts taken by both sides before the result. With regards to health care, the Democrats have been expending huge amounts of political capital over decades trying to move the health care system towards single-payer, while the Republicans have been resisting such change. The Democrats finally succeeded with Obama's reforms, and Republicans have been desperately hoping it will crash and burn, and repeatedly trying to or threatening to repeal it given the first chance they can; they even tried to get the Supreme Court to declare Obamacare unconstitutional. Your claim that both sides want the same thing makes no sense.

The direction the parties are pushing policy towards are what makes the party. Remember when Bush tried to dismantle Social Security, to the cheers of practically no-one?