Dems acknowledge that they govern by the will and wishes of their people, most of whom are in favor of legal, vetted immigration. So, the abuse of the asylum process, which does happen, is a genuine problem that needs to be addressed.
Neither of the major parties, nor the bulk of the populace, think the borders should simply be completely open though. That's a repub talking point to smear dems, and is a lie.
Bureaucracy and process are good things. Everyone just doing whatever the fuck they want, whenever the fuck they want is not.