While i'm not an expert in regards to this, I do know that publishers are more than likely not going to look at anything unless you have a great deal of the game finished. This is for a variety of reasons, including some of the problems you mention in your post.
The more reputation you have though, the more likely a publisher will not pass you up, so if something has an audience, a publisher wants to hear about it, because they are less likely to accept something which would only apeal to a handful of people.
If you do get a deal with a publisher, chances are they'll be taking a large portion of the profits for the work they'll do to sell it.
A nice thing about casual games and their market, is it is fairly easy to setup a site where you can sell your game and not have to worry about publishers all that much. But if you want to aim higher and go for say a handheld device or something, you'll need a publisher to handle all the packaging and marketing and all that crazy stuff i think.
I think the biggest thing about getting a publisher would be the actual game itself. If it means money in the eyes of a publisher, they'll jump on it. So presentation and research is everything if not something..
edit: Also, i've known people who have gotten publishers to lend them money to hire people and makethe game because the ideas were good. so, it varies..
edit2: You can try making demos of games to show to publishers, and if they like it, you might get some help to fund its development. you'll have to pay it all back though once the game starts selling, plus more for the portion they take to publish it.
