Hi there.  My mix environment sucks and it shows in my mixes.  In the near term, I will not be able to change this fact.  Is anyone else in the same boat?  Does mixing using cans work for anyone here as the primary method of mixing?

I mix on cans ALOT for a myriad of reasons.  But for FINAL or PRECISE mixing, fidelity, mastering, EQ-ing, etc. ... Studio listening (Adams speakers, ARC, etc. etc.) becomes necessary for generalized translations.
 
If you can't change this fact (?) you'll need non-EQ-biased cans, like AKA k702s (iirc), or similar.  I'm pretty sure others here will recommend appropriate cans for your dilemma.
 
Also, having several sets of cans may help; pairs you know might render the lows mids &/or highs for your peculiar needs.
 
Note: For me, the NOTS: Ear-buds (even the best) ... are a no-brainer.  They hurt the ears and never perform as advertised (for me).  Noise-cancelers (like the Boss Quiet Cans) likewise suck for translating per se (despite being great for noisy environments).
 
Hope this helps.

A good set of phone and a Focusrite VRM Box are a worthy investment if you're going to be doing any mixing in cans.
 
Rocky

Awesome!  Any specific recos on a model of headphones that won't break the bank?  Suitable for rock music?

if you mix in cans, you'll get screwed by comb filtering.
 
in other words, you'll never hear it.
 
til you hear the playback on another system and say what the phuck

I like to mix in cans, even though I have excellent speakers in a nice-sounding room. The cans are like a second opinion. If it sounds good in the cans AND on the speakers, it gives me a high degree of confidence.
 
My current favorite headphones are the ubiquitous ATH-M50s. They do a fine job, they're comfortable, rugged, and inexpensive (~$150). A little hyped in the low end, but I've become accustomed to that so it doesn't get me into trouble.
 
Lately I've been thinking about adding another pair of headphones to my collection, mainly just for pleasure listening but also as a third reference. Something that complements the Audio-Technicas. So I've been researching and listening to many models in my price range (< $300) and at the moment the Shure SRH-940 (~$250) is at the top of my short list. 

Well these days I mix in the cans almost entirely, mainly because I live in an apartment.  A couple of things though, firstly I do it with a couple of spectrum analysers, this way I know what the mix is doing.  Secondly I know what the mix should look like when using a spectrum analyser and thirdly I use open back cans which help with the stereo image.  My cans are Beyer Dynamic DT990's.

I pretty much mix entirely in headphones. I have some Shure SRH1840's. They are open back and i love them. I prefer to mix in headphones but as others have said, you have to check your mix on other systems.

Focusrite VRM Box is well worth the price to help save you on headphone mixing heartache.

Personally, I can't stand mixing on headphones.
 
I find them really useful for checking stuff but:
a) I couldn't stand working with headphones on for that length of time
b) your stereo imaging is all over the place