Of course the US has legislation to control the border. There is an entire agency called the border patrol. The thing is right now , it seems, additional legislation is needed to actually compel the executive to have the border patrol do their job. Which this last bill didn't even do and would have simply dumped money into an auxiliary judicial system that serves virtually no purpose and would continue to do so even with more money. Shortening the time for an asylum hearing doesn't even matter because people don't show up for them.
Any bill that maintains the current administration's position of simply letting people go completely free during their asylum waiting period is useless. Sure, people with legit claims might show up, but crimminals, which are the problem, are not going to come back for the hearing.
Most Americans don't mind immigrants or immigration at all and not even the idea of illegal immigration is really a problem. It's just the people that commit crimes that are the problem, it's one of the reason we see recent immigrants be so strongly in favor of border security, because the people they specifically tried to get away from are showing up too.
Not only are people caught crossing the border illegally not detained, but apparently even when they commit additional crimes it's too much for some cities and states to even keep them in jail for those crimes.