Lets examine each proposal by the Dems:
The expansion would include online firearms purchases and those from unlicensed dealers at gun shows.
Online firearm purchases are already covered by existing gun laws. You can't send a gun through the mail unless it goes to a FFL person who then runs a background check before the transfer of the weapon can take place.
Unlicensed dealers. This can be a misnomer for someone selling a single gun at the show as most states require a FFL to have a spot at a gun show. This should be left to the states to decide, not the federal govt.
Under existing law, the F.B.I. has three days to provide evidence that a gun sale should be prohibited. If there is any delay, the sale can be completed on the fourth day.
They say this could have prevent Dylan Roof from getting a gun. Was it ever stated that if the wait time had been a week that he would have been denied? Was there information in a database somewhere that would have been found to prevent him from getting a gun? They also say over 15000 purchases were made and would have been prevented if not for the 72 hour limit.
That measure, sponsored by Senator Patrick J. Leahy, Democrat of Vermont, would expressly prohibit straw purchases and stiffen penalties for making false statements in connection with gun buying.
These things are already all illegal. The problem is the DOJ doesn't properly prosecute these types of cases. Increasing the penalty, jail time, would be a good idea but you actually have to do it.