The phrase "logrolling" best describes when a lawmaker strikes a deal with another lawmaker to pledge to support their proposed legislation in exchange for support of the other lawmaker's legislation.
Quid pro quo best describes the idea of logrolling in the current American political system. Politicians that engage in logrolling swap their support for a particular topic or piece of legislation for the support of another politician, often through parliamentary votes.
A lawmaker who logrolls starts the exchange of votes for one specific act or bill in order to get support for another act or bill. Logrolling is when two parties agree to back each other's positions so that both pieces of legislation may pass with a simple majority.