As we were taught in school, we should be very skeptical when any legislation goes before the U.S House of Representatives. Most bills die in committee before ever making it to a vote. If it somehow manages to come up for vote in the U.S. House and pass, it is not at all likely to make it through the U.S. Senate. Keyword: IF.
If it makes it through the Senate, it will not look the same, and at the very least it will have to be voted for approval in the U.S. House again, since it has been changed.
Regarding the sitting President's political capital, study it. If you think Presidents Obama, Trump and Biden had or have unlimited political capital with Congress, that's not true at all. Look at each POTUS as having limited polical capital in Congress. When they swing hard for one bill, they have used up a little or a lot of their capital for their 4 year term.
The proposed ban mentioned by the OP has too tall of a mountain to climb. Not big, that mountain is enormous.