We all have to submit to a background check when purchasing firearms. What they propose is delaying issue until the person on the list has been cleared by the FBI. The FBI will be given a time limit to either file or drop the case.
Many states have mandatory wait times for firearms. This would be no different other than it would only affect those under FBI investigation.
And many States have explicitly REJECTED mandatory wait times for firearm purchases.
Not for transfers for example between friends and family members.