Funding opportunity announcements from the NIH come on both vague and highly specific flavors. (For the latter, think "We invite applications examining Gertzin trafficking in the Tiddle cells of the Physio-Whimple nucleus during bunny hopping. Applications using the 100m to hedgerow model will be judged responsive.")
One of the things that I've slipped out from under far too slowly in my career is the naysayer voice "There's no frigging way I'm going to be competitive for that!"
And yet...circumstances have occasionally pushed me. To venture an application that in my heart of reviewer hearts I think is such a long stretch as to be nearly a waste of time.
Interestingly enough, I've gotten a grant that way on more than one occasion.
Edited to add: It was Damn Good Techncian who pointed out "getting published in Science is like a threesome - if you don't ask, it won't ever happen.". This also applies to grant applications according to drisis.