Attitude is at least half of a comic's act. Attitude, in the comedy circles I ran in, was more often called "persona". A comic is giving a little play to the audience he's performing for, so he assumes the mantle of a character. As all writers and actors know, the best characters are consistent. A stand-up act should be the same way: as a comic, when you're on stage, you should have material that seems to come from one person's vision. Of course, the trick is that all of your jokes really do come from one person's vision: yours.
But you'll find, if you write stand-up, that sometimes you'll write a joke that just doesn't seem quite right, doesn't fit in with the other jokes you do, the way you like to perform, the way you use words on stage and so on. An extreme example would be Andrew Dice Clay going on an extended bit about how much he loves his wife. His whole act is misogyny, misogyny, misogyny so if he plugs in a five minute bit where he's Mr. Sensitive, it simply isn't going to work. So his attitude, the persona of misogyny that he has crafted, definitely steers his act...
Think of just about any comic and their persona is in perfect accord with their material:
-Carlin does jokes about oddities and stupidities and his persona is exasperated (if you're the only one who sees the stupidity, you'd naturally be exasperated by it).
-Brian Regan does slice of life, very clean material, so he seems like a normal everyday, very personable guy.
-Bill Hicks is confrontational and seeks to destroy preconceptions so he's very emotional in his delivery and uses cursing and expressive body movements, like a crazy prophet.
-Steven Wright looks at everything very literally, so he has what appears to be an absence of persona/attitude - he simply says "this is the way the world is" and engages in no hyperbole or "extras" because his vision is so stark and bare.
Ya constantly hear comics talk about finding their voice. Lately I've been thinking how a big part of that is what you say no to. How the jokes you don't tell are just as important to your voice as the ones you do tell. Telling a joke that gets fewer laughs but fits your persona can be a smarter move than telling one that hits hard but seems out of character. Or maybe you have two different "styles" you can work in (one-liners vs. longer bits, angry guy vs. crowd pleasing guy, high status character vs. low status) but you're better off dropping one so your whole act feels more consistent.
Tangent: I recall hearing Birbigs in an interview talk about the challenges he faced moving to theater shows. One of the things he said was toughest was throwing out jokes that he knows will get a laugh. His director made him get rid of anything that didn't move the story foward. The narrative was more important than laughs per minute.
Tangent++: This review of John Mulaney's album includes this take on Mulaney's "comedic persona" — or lack thereof.
What I like about the album -- and about Mulaney in general -- is that he doesn't have an obvious "hook." He hasn't gone to great lengths to create some comedic persona or be known as the "fill-in-the-blank" guy. That doesn't mean he doesn't have a voice (something I've harped on other comics for in the past). He sees the world with a bit of amused detachment, and is simply funny in an unassuming way. Sometimes, funny is enough.
There isn't really an easy way to sum up Mulaney's persona. Maybe he gets away with that 'cuz he's such a damn good writer? Hmm.