Who? Bear in mind that in the inevitable disruption that happens, there will be an opportunity to do something different.

Both Democrats and Republicans. On the Democratic side, it's been the progressive wing. They were philosophically opposed to the idea of a permanent "underclass" of residents who neither had the rights of citizenship nor could ever achieve citizenship, but did the dirty, difficult, and/or dangerous work that often falls to uneducated workers. They also felt that such workers would be vulnerable and exploited by their employers, since they would have such tenuous footing in their jobs. Echoes of the H-1B complaints we've seen recently.

On the GOP side, it's been the cultural conservatives/nativists who don't want the U.S. to open up to large numbers of immigrants. If you bring in a few million people as guest workers, a non-trivial number of them will (over time) have children or get married or make community ties or a host of other things that makes them likely to stay. Or just overstay their guest worker visa. They want to keep them out.

Would a disruption that undermines the status quo create an opportunity to do something different? Probably not. The reason that our immigration system is a kludge isn't because a majority of people like the current system. It's because there are too many alternatives, and none of the alternatives has anything close to majority support - and since our political system almost always results in inaction when there isn't a majority consensus in favor of action, the most likely outcome is usually inaction.