While there are many formal models that generate predictions about polarization, only a handful address the question of how, with no change in electoral rules, levels of polarization can dramatically vary over time, as they have in the US House during 150 years of two-party competition. We propose a model that emphasizes national party constraints on district candidates’ ability to locate at positions far from the national party stance. The model predicts a close relation between tight tethers maintained by the national parties and congressional polarization, suggests implications for political competition, and generates the empirically accurate prediction that partisan polarization and within-party differentiation are negatively correlated. When the tethers of the two parties are not equally strong, the model suggests modifications to the conditional party governance approach and helps explain ideological shift/drift affecting both parties, with the party with the tighter tether moving the other party toward its ideological wake.