While there is probably no such thing as "too long," 22 words would be considered a very long heading.
Assuming you are doing this for style purposes, there is probably a better way to handle your tagline than with an H2 tag, which should be the second biggest and most most notable thing on your entire page. Stylistically, this isn't usually how taglines or slogans are displayed, even on websites. Just because it's in the header doesn't mean it's a heading. Think more like how a newspaper page is laid out. The H1 is the top, bold, big font, headline at the top of the front page. The H2 tag is the second lead story. The H3 tag is the sub-headline for that H1 story, and so on.
Assuming you are doing it for SEO purposes, then you are wasting your time. It is generally accepted that Google only crawls a certain number of characters in the title tags and header tags. If that is accurate, then all the words at the end of your your tag are going to be ignored anyway.