Non-meme answer: both Republicans and Democrats have party whips (other parties in other countries, too, but talking about the US here). A whip is a member of the party who holds office in congress and there's one for both the House and Senate. They are appointed by leaders within the party.

A whip's job is to make sure other party members vote alongside the party platform. They do this in a variety of ways, such as offering to make changes to bills or threatening to withhold election funds for a person's reelection. Their role is an enforcer. Party members who step outside of what the party wants voted on become targets of the whip's attention.

This is generally seen as a full-time position and as such, whips may spend less time involved with congressional committees or drafting legislation. A whip and their staff will use most of their resources on enforcing party discipline.

It's how you know Democrats are full of shit when they talk about "not having enough votes," even when their party occupies the most seats in congress. They have two whips whose full-time job is making sure everyone votes consistently with what the president and other party leaders want done. If a whip is ineffective at enforcing party discipline, the party can appoint a new whip immediately since it's not an elected position.