Get around to <something> means: to do <something> after you have intended to do it for some time.
First Question:
Can we say "when you can get around to it."? Or is the meaning of "can" already hidden in the idiom?
Second Question:
Where does its meaning (the one mentioned above) come from?
Best Answer
Short answer: 1. Yes. 2. The meaning comes from its words.
To get (a)round to is a phrasal verb: The origin of the meaning is simply found in its words.
The Oxford English Dictionary defines both to get around to and to get round to as phrasal verbs, having the same meaning:
Without the to, the verbs diverge in meaning, as you can see at the end of this post.
The earliest recorded usage in the OED is from
followed by P.G. Wodehouse in Laughing Gas:
which is an interesting quote also because of was aiming to, which means
The first usage is from 1400, so this goes way back. But it used to be a regional thing; it is now considered colloquial.
Before WWII Wodehouse lived in both the US and England; he often represented "the English" to American readers and vice versa, publishing books in both countries. Wodehouse had a 75-year career as an author. Astonshing. Even in some of his later works he uses expressions found in his earlier works 70 years later, when the world had been a different place (before both world wars).
The first genuine usage for get round to is 1946.
Notice the quotation marks around the phrase; this indicates something about the attitude of the phrase by the narrator of the story. Perhap he means the phrase is new-ish or that its usage is ironic. (By the way, Wodehouse has a lot of uses of words with the ending -ish, showing that this suffix is not anything new, despite its recent resurgence in use.)
As Jasper has shown, we can use can before get around to, just like we can many verbs, with the sense of being less direct or more polite. To see this meaning of can, try it as an imperative (an order):
These are actually orders, but the can significantly softens them.
So, you know
Without the to, the two phrasal verbs have other meanings:
to get around can mean
Note that today if we said "Mary Jane sure gets around," it would often (always?) implies that she sleeps around (has sex with multiple partners, or is at least alleged to). So you can see how the meaning has changed from 1928 to today.
to get round can mean:
The idea, I imagine, is to get round a disease and make it back to health. But I can't recall this phrase actually used this way. Nowadays, we say come (a)round (apparently only an AmE usage) or, using a different verb pull through.
I wouldn't use this phrase to have this meaning, as it seems outdated, although the OED does not indicate it as such. But come around is used today, as is pull through.