As I understand it, these laws are more designed to go after the websites that "knowingly assist, facilitate, or support sex trafficking"  They're not trying to prosecute the sex workers themselves.  (which, IMHO, is the big problem with them.. you want to stop trafficking?   Go after the Traffickers!  Now you're just driving them underground so harder to locate.  Stupid law from stupid people)    

It's more the issue that if you pay for the ad, you'll loose money if the site goes down.  

From my understanding, since City Source is locally run, and they screen everyone who advertises, I don't think there will be much chance of someone trying to prosecute that site.  It's generally more the Backpage or Craigslist sites that was the bigger worry.  Though sites like CityVibe are just being proactive and shutting down early.

Remember also, while the House and the Senate have passed bills, the two bills need to be reconciled (they are different) and then the President would need to sign them before they become law.