No.
By the same token, you could say "hey, let's cut off social security until we've screened out all the frauds". Or "hey, let's cancel all airline flights until we check out those chemtrail claims". We have a screening process in place. We can work to improve it without cutting it off entirely for who knows how long.
Mind you, I'm not opposed to making it more difficult to immigrate to the US. Fine by me. But there are plenty of people who are trying to get here legitimately, and it would be unfair to block them due to an overreaction.
Now, if it turns out that Trump went and fired half the screeners, that's his own fault.