It probably won't even get through the Senate committee. It's virtually the same bill that didn't make it through the Democrat controlled committee last time.
Have you read the bill? It would require all private transactions of handgun sales to be conducted through a FFL, and the FFL would have to call DOJ just like for his own sales, and pay the $13 fee. The FFL passes along this fee to the buyer, and is limited by this bill to a $5 transfer fee for his time. That's rediculous. AFAIK, FFLs are NOT required by ATF to perform any transfers that are not their own sale. They are allowed to, if they so choose, and they may charge an appropriate fee. If I were a FFL, I'd be insulted by this. My time is worth more than $5. I sincerely doubt most FFLs would partake in this (unless it was a "favor" for regular customers or friends), and I don't blame them one bit. I wouldn't do it.
So what happens if people attempt to follow this law, but cannot find a FFL willing to do the "transfer" for $5? They'd likely just go ahead and sell the gun if they know the person buying it. In the more rural areas, FFLs are few and far between. I'm not driving all over the countryside to find someone willing to do a "transfer" for 20% of the going rate... then drive back again in 48 hrs if I'm the buyer? Not likely. If the gun is "in circulation" prior to the effective date of such a law, there's no way to prove the sale didn't take place prior to the law. Both parties would be illegal, so nobody's talking, and cannot be forced to either (5th Amendment). "Screw this... here's the cash/gun, give me the gun/cash" is how most transactions would take place. This is one law that would be very difficult to enforce, and I have no doubts it would be widely ignored by people selling to friends or family.