No - the 15 to 20 days was put in place when travel was much more complicated than it is now. It was to give the cardinals a chance to get to Rome from wherever they were.

It's possible he had some serious health issue where his doctor said resign ASAP, rather than just generally he is too old and frail to do it. But either way, even if he just thought I'm outta here, I think the idea was that he expected a new pope to be in place by Easter and the Easter mass (which is a big deal there) will be the new Pope's "unveiling" to the public, his first big hurrah. I think they should be finished by Easter, that is what I've head all the pundits say. Because it would be truly bizarre to have a vacant pope chair during Easter, I don't think he would have wanted that.

"Conclave-should-start-March-15"

Cave Idus Martias.