What, if anything, would prevent a majority party in Congress from simply refusing to seat newly elected members of an opposing party?

Political consequences and a respect for the institution. In a republic, there isn't a safety net if the people in power don't make each other follow the rules. Monarchies, like England, did: the king. The king's ability to dismiss parliament was seen as the guard against "tyranny of the majority", basically an out of control parliament that infringes on the rights of their political opponents. The logic behind the king having that power is the same reason our judges have life tenure - an attempt to remove all political or personal motivations.

"Checks and balances" doesn't mean the founders thought through every possible scenario that may come up in the future. It is a metaphor for how the three branches could regulate each other's behavior without needing a king.

A system of checks and balance between the legislative and executive branches would use each branch’s “ambition” to check the ambition of the other. As Madison famously wrote, “Ambition must be made to counteract ambition.”

Madison believed that the competing “ambitions” of the legislative and executive branches—and the people in them—could be used to protect the judicial branch from being overpowered. Madison saw the judiciary as having “peculiar qualifications”: at is, goals and objectives different from those of members of the legislature and executive branches.

/r/Ask_Politics Thread