Duverger's Law indicates that plurality (first past the post) systems devolve into two parties per seat, while proportional systems support many parties. Because the United States has a national presidential election, this essentially forces the US into a two party system.
If the US switched to a proportional system, it would make it easier for third parties to get more votes and seats. Those seats would have to come from the Democrats and Republicans because the two parties have almost all the seats (currently 98% of the Senate and 100% of the House). Since both parties would lose seats, both have a vested interest in avoiding a proportional system.
Individual members of either party might be more open to the idea. The ones who are the most interested will often be those most likely to join a new party.
In the 2017-2018 Congress, the Democrats control 47% of the Senate and 45% of the House of Representatives while the Republicans have 51% and 55% respectively. Contrast that with Germany, where the largest party is 32.9%. Other proportional systems have similar results. No one party controls a majority of the seats
Out of power, the Democrats have more incentive to shake things up, but they also have the broader coalition. They are in many ways more vulnerable to a proportional system than the Republicans. In Germany, the second largest party is only 20.5%. This is why they tend to concentrate on reforms that increase their influence relative to Republicans (e.g. the Fair Representation Act or efficiency gap analysis) rather than reforms that reward proportionality.
Now, sometimes the larger parties do better than at other times. Before the latest election, the two largest parties in Germany controlled 41.5% and 25.7% of the seats. And of course the Democrats may find that they would still be the largest party in the coalition.
Meanwhile, the Republicans are a majority in both chambers of Congress and control either the governorship or at least one chamber of the legislature in most states. They might be the largest minority party under proportional representation, but they would still go from the majority they have now to being smaller than they were when last in the minority.
There are countervailing advantages. For example, if congressional Republicans and Donald Trump were in different parties, they would be less beholden to the president. And they would have more options in coalition building. But apparently they don't value that as much as they do the current system, where they are at worst second.