I certainly understand the sentiment, but my question to someone on the "anti" immigration side would be this: what do you see as a possible alternative solution?

Most people are not against immigration per se, they are against uncontrolled immigration of undocumented aliens. A legal and orderly immigration process is the way to go for Europe. In fact this route existed for many years but recently it takes a back seat to simply running over the border. Europe need to scale it up and actually allow for more legal immigration.