The billboard, along an Interstate 70 business loop in Grand Junction, shows the four figures around a table playing cards and rats below.
The sign reads "Vote DemocRAT. Join the game" at the top.
Mesa County Democratic Party Chairwoman Martelle Daniels calls the billboard racist and homophobic. Her GOP counterpart, Chuck Pabst, describes it as "juvenile" and "reprehensible."
The artist, Paul Snover of nearby Loma, tells The Daily Sentinel in Grand Junction that he's not allowed to say who paid for it.
He says he would have included Republicans as part of the problem.
Many motorists have been pulling over to take pictures of the billboard, reports CBS affiliate KREX in Grand Junction.
Some just shake their heads, while others have a lot to say about it.
They say that, although it's a comic painting, the message about the president is disrespectful and in bad taste.
But Snover says it's a good example of using First Amendment rights to poke fun at some national issues.