Panama is not even remotely close to being able to handle such a gargantuan expansion in its buacracy. The Panamanian government would find itself extremely overstretched and unprepared for such a massive expansion and as such would run the risk of collapse.

There are only 2 or 3 countries whose state administrations are possibly big enough to handle the rapid expansion in their buacracy: The United States, Brazil and Mexico. But between those 3, the US is the most likely to be able to pull it off as it is already the most populated and expansive state in the hemisphere and has a tried and proven method of expansion (essentially granting statehood to placed and then shuffling congress around) whereas Brazil is not known for having strong and reliable democratic institutions and is also known for being somewhat inept, and Mexico is incredibly unstable and struggles to keep its own territory together outside the major urban areas.

Meaning the best bet would be the US annexing and granting statehood to the continent(s). Ofcourse depending on the size of the country, Nicaragua can be admitted as a single state but Mexico, Canada, Brazil and Argentina would likely have to be broken up into their states and state equivalents and have those admitted instead, and have medium countries like Colombia and Peru broken in half and admitted that way.

The issue here though is that most may be hostile to US-American annexation so a better solution would to create an EU-style system and progressively increase its powers and duties until it inherits the militaries and international diplomacy of its members, forming a confederation.