Which term describes a situation in which Democrats and Republicans cooperate to support common goals?

The term is bipartisanship.

Explanation:

If the two parties agree on promoting a piece of legislation together that enjoys wide support within each of them, we speak of a "bipartisan bill."

Or if Congress declares war on a foreign country unanimously, then we say that the declarion of war was an act of bipartisanship because all Congress members, no matter which party they belong to, voted in favor.

bipartisanship

agreement or cooperation between two political parties that usually oppose each other's policies.