At the general election level; yes, you'd need a constitutional amendment. At the party primary level, however, such a system as you describe would be incredibly helpful, and probably for all parties.
How? A proportional representation system only works if you have multiple people elected into an office for any particular constituent.
The Republicans can't nominate 100 different people for the 3rd congressional district in Florida. Well, I guess they could, but then the first past the post system would practically guarantee that none would be elected, and that is why they only nominate one.
In a proportional system the Republicans would offer a prioritized list of 435 representatives for the entirety of the US House, and then their members could use proportional voting to decide who ends up in what slot. Then in the general election the Republicans would be awarded some number of seats, and the top n candidates would take office.
The president would still lead to the usual deadlock if separately elected since it is one man in one office. The only real solution to that is to replace the office with a prime minister, which is of course how most democracies handle the situation. That would require an amendment as well, and probably a rewrite of half the constitution.