According to news reports, the current administration is contemplating sending the illegal aliens to the sanctuary cities. This is not getting a good response from these cities, but they decided sedition was better than the legal process, so they're complaining.
The best solution for stopping the influx is finding those financing the aliens, and removing their ability to provide support. This, of course, will require some brutal solutions, but such people can best be described as enemies of the United States, and treated as such.
As far as those already here? It's cheaper to send them back. The expense is far less than allowing them to be parasites on the U.S. economy. Round them up, prosecute anyone aiding their illegal entry, and stop the problem before it becomes worse.
I know some federal judges will attempt to stop any efforts to rid the country of the aliens, but they can be ignored. They have no standing in matters of national security, and their power doesn't include ignoring laws they don't agree with.