In my part of the world, to even have a juke box, or one man band play music in an establishment, the owners must belong to ASCAP. I was in my local pub years ago when a suit walked in and shut the music down, and unplugged the juke box. The owner was also told not to play VH1 or MTV until such a license was obtained. In many cases the Juke box vendor will obtain the license for his machine but the bar owner must take care of the rest.
Yes, ASCAP are very much present in the US and are often complete bullies! Any club that has live music is constantly threatened by lawsuits from ASCAP and BMI. Many clubs around me only allow original music now, and some have just cancelled live music altogether. The problem isn't just one group, it's both, and the fees are high. Even if you don't have live music, they charge you for TV and radio. If you convey TV or radio signal over more the 6 speakers at a restaurant/bar, you have to pay ASCAP fees.
In Europe, they have a similar organization called SESAC which does the same thing. They have employees who show up undercover at bars and clubs to see if they have music, and then report them to the organization, who starts legal proceedings. It's extortion-like.
Now, it's worth mentioning that I've done union gigs, and am generally a fan of the Musician's Union and the Pay for Play movement. I think artists should get paid for their work, but the licensing doesn't always work out. The fees are calculated based on the number of nights music is played (recorded or live) and the max capacity of the club (based on the fire department).
As a result, several cafes in the area can't afford live music anymore. Even if they have only original music, BMI or ASCAP agents could be there and if they hear even a reference to copywritten material, they'll file a lawsuit.