Can the State compel an "artist to paint a picture"?

Recently, Attorney General Bob Ferguson filed suit against Arlene’s Flowers and Gifts of Richland, Washington, for refusing to supply floral arrangements for a gay wedding. State law requires businesses serving the public to accommodate customers without regard to sexual orientation.

There is no question the florist violated state law and that the Attorney General has both the authority and duty to uphold the law. The question is, can public accommodation laws be applied to creative expression without running afoul of the First Amendment? An attorney representing the florist thinks not, characterizing application of the law in this case as

“compelled speech in violation of the First Amendment. The state cannot require a florist to express appreciation for, or acceptance of gay marriage any more than the state can require a musician to write a song about it, or an artist to paint a picture.”

I find this argument intriguing. If I were an artist that painted wedding portraits, could the state require me to paint a picture? Wouldn’t that violate my right to free expression under the First Amendment’s umbrella of free speech? If so, wouldn’t that invalidate state public accommodation law when applied to the creative arts?