The fedgov exceeded it's Constitutional authority a loooong time ago...to worry about it now, in the context of Smelliot Spinster is closing the barn door after the horse is in the next county.
In this case, I think the feds actually have legitimate concerns. Tens of thousands of men might use prostitutes every day, but few of them are in the position to be blackmailed over the security posture of a large state containing the world's financial hub. That the ex-governor got hoisted by his own petard is not only, IMHO a legitimate exercise of authority on the part of the feds, but also poetic justice in a very karmic way.
FWIW, as a Louisiana resident, and generally a supporter of him, I posted this about him last July...
"If there's enough evidence to charge him with solicitation, charge him under LA and DC law, and let the chips fall where they may."
...so at least, I can claim philosophical and intellectual consistency, even though my feelings towards the two men couldn't be more different.
Blackmail is a good point.