On various occasions I have heard somebody in shul declare that they have a chiyyuv to daven - an obligation, that is, to serve as sheliach hatzibbur: to represent the congregation in their leading of tefillah. To be honest, I've never actually understood what constitutes this chiyyuv, and have guessed (though am probably wrong) that it relates to an obligation to say the amidah twice.
Is there really such a thing as a "chiyyuv to daven"? When does a person possess this obligation, and how much of the davening does it require them to lead? I have only ever heard people say this during shacharit, but does it apply to mincha (and to maariv) as well? Can it be limited to mussaf, on a day when mussaf is read?
Secondly, what happens if there is more than one person in shul with this chiyyuv? Is there a scale of obligations, with some chiyyuvim trumping others, or are all obligations equal?