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

bipartisanship

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

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.