In an answer on ELL it reads:
Here – and this is a reach – but it could technically be understood to mean that my mother thinks this girl is the prettiest I can find, though there are prettier ones out there in general.
In that context it sounds to me like this statement makes some reservation, for that reason I believe the meaning is "far-fetched" as in "The whole story sounds very far-fetched."; in other words, that it's unlikely to be understood in this way. And though, the opposite meaning might be equally likely.
However, trying to confirm one or the other by searching the Internet, especially dictionaries (Oxford Dictionaries, Merriam-Webster), I can't find anything which gives me a clue.
Reach undoubtedly means the distance over which something or someone is – well – reachable but then I actually expect a saying (with the meaning that I suspect) to be like "This is out of reach" or for the opposite "This is within reach"; but in any case I wouldn't go with "a reach".
So, what is "a reach"? Is it something I can achieve because it's still within reach, or is it something I won't achieve because it's beyond reach?
Best Answer
Haha, that was me. Sorry about that, I shouldn't have used such a phrase on the ELL site.
You do understand the meaning of the phrase correctly (apart from the "opposite meaning might be equally likely" part perhaps) - it does mean something along the lines of, "and this far-fetched, but I'll say it anyway". As such, a reach is closer to "something you can achieve because it's still within reach", though "far-fetched" fits better.
In terms of definitions, I would say this definition of the verb to reach (then changed to a noun) would be closest / most applicable:
Here are some other sentences with this use of "to be a reach", taken from COCA:
I find this last example is particularly helpful in exemplifying the meaning: counsellors recommend that high school students apply to 6 colleges; the first two are the ones you really want to get into, but you doubt you have a chance (but you might be lucky and get in, so you should try just in case), the next two are colleges that you think are at your level and so you have a good chance of getting in, and the final two are colleges that you are less impressed with, but you think you'd easily be accepted. The reasoning is, if you get accepted to a college that is a reach for you, you'll likely go there. Otherwise, you'll go to one of the colleges in your range assuming you got accepted there. If not, you'll consider going to one of the last two colleges, since there's a pretty big chance you will have been accepted to those.
Note also that "a reach" can be used in other circumstances that don't necessarily mean literally reaching for something: for instance, a hockey team could be said to be "making a reach for gold".