There is not sufficient evidence that introducing waiting periods decreases gun deaths.
Waiting periods put citizens at risk. Consider a situation where a citizen felt threatened and believed that their husband was mentally unstable and plotting to kill her. She cannot go to the police on a hunch without evidence. But she is vulnerable and knows she needs to protect herself.
She drives to her nearest gun shop, only to find that she must wait three days before she can bring her handgun home. That night, her husband kills her.
This argument was what prompted lawmakers in Wisconsin to consider revoking the mandatory 48-hour waiting period on gun sales in the state.
Instant background checks now make waiting periods redundant. There are also already mechanisms in place to prevent someone buying a gun and committing a crime of passion. Most gun sales cannot be completed in under an hour. This is plenty of time to cool off. If a person still commits murder after an hour of cooling off, the crime was premeditated and not a crime of passion.