Congress has passed unconstitutional laws before.
It will be up to the people, including organized people like the ACLU, to find a test case and challenge it. Ironing it out will be the courts' job.
Meanwhile, We The People can petition our congresscritters to reinstate this provision, with the unsubtle suggestion that some of us might become one-issue voters on this issue.
I'm rather fond of the Bill of Rights, myself.