The problem is downstream liability -- a website may have no practical way to verify ages, without an operation requiring a lot of economic scale.
The law might run afoul of Section 230 of the 1996 Telecommunications Act. On the other hand, the law appears restricted to ads, which makes it much narrower than was, say, COPA.
Anderson Cooper is discussing the matter June 7 on CNN on his AC360 program.
CNN has an editorial by Douglas Rushkoff opposing state laws like this, saying even CNN could be liable if a visitor's comment amounted to an illegal ad. Here is the link.
ABC News has a story about the challenge to the law by Backpage, (website url) here. On June 5, a federal judge placed a restraining order on the state law.
Tracy Clark-Flory has a story about HB 6251 on Salon here, and notes that the law only requires an "attempt" at age verification -- a concept that we know failed with COPA. Salon was a COPA plaintiff.