Pinpoint  your other qualities and say you're a fast learner.

I do try to do that. Firms do want some one who can jump in though without a lot of hand holding. 

I mean, I tell them I'm a fast learner but that I would need a bit of a learning period.

Get some experience. Take on some craigslist drafting jobs and do them in Revit. Many areas offer full day beginner training to get you off and running or lynda.com or...

Does the local community college offer a course on Revit?  

Find an office that's only starting to use Revit and work for them, I'm sure there are plenty of those around.

I don't really think you need to take a class or find a drafting job. I was in the same position a year ago, I had just graduated with one quarter long class of Revit, and looking for a job in Seattle. There are plenty of firms out there and a lot that don't use Revit yet. Look for smaller residential firms, go to the AIA office or look online. If it is a Revit based firm they just want to see that you can produce CDs, a lot of which you can learn via YouTube on the fly. I honestly think you'll be fine, just keep applying and reaching out. 

if that's the primary consideration, maybe that's not a place you want to be long term

good firms will recognize that they'll have to do some training and search for candidates that they see a good future with, not just some immediate production drafting

Every firm will have different standards for drafting and modeling, so there will always a be a learning curve for any new hire regardless of software experience. You can hide some of your ignorance under the guise of asking how they would like something done.

Really the only way to learn well is to jump in and just do it. I wouldn't lie. Don't say you have experience that you don't have but downplay the amount of time / number and scale of projects and play up the fact that you are self taught and are eager to continue to develop your knowledge of the program. 

In an interview when the question of revit experience pops up you need to say something along the lines of : " I'm self trained but always worry that there is a better way of doing things then what I have discovered, my ability to learn software on my own also means that I have the ability to hunt out and provide answers for myself, it also makes me excellent at trouble shooting which is a huge part of working in a revit. You are excited to learn from and contribute to their revit team" 

that ought to do it. then you just have to work your ass off to stay to speed. use lynda, youtube, forums, ect. to make sure you know whats going on and are following through on your promise to find answers and self teach. chances are you will learn new things and actually be a contribution with an attitude like that. which is far better than a cad monkey with ten years of experience. 

The sales pitch is:

Revit is a tool.  You can teach anyone to master a tool, but it is difficult to find someone who can imagine and know what they should document using this tool.  That is where you fit in… and present the portfolio and the experience.  A detail, elevation, and everything else in a drawing set isn’t what the client buys; they buy the thoughts behind them.  Sell them your thinking is better than some plain ole cad monkey…. Sell them you need less direction on what you are trying to draw.

Basically, most firms would choose someone who knows how to put together a building over someone who knows a software program.  Think of it this way; in my 30 years of experience, I’ve seen handdrafting, early cad integration (mixed media), autocad and extensions, 3d autocad modeling, then REVIT. (software & tech changes rapidly.. duh)

I, and most firm owners know, it’s not the software that is hard to master; you’ll be slow for a month… not a big deal if you know what you are drawing any why.  In the same30 years, windows, doors, walls, etc. haven’t changed significantly in how they go in a building and are detailed.  Sell them your experience/knowledge is more important and why you should be hired. Don't get hung up on the hardware/software... it's a false idol.

^^Fully agree with mightyaa. Our firm has been burned more than once by software experts that didn't understand production drawings. Try to convey that you'll catch up at Revit far sooner than you'd make up for being overly green when it comes to buildings.

the issue with Revit, as I myself am learning the program, is that it really is a broad and deep one, with many tools here and there, and options the deeper you dig. and so, while it is good to pick up the tools on the way, the working process is a specific and learned one.

so, after getting acquainted with these tools and options, I find this really quite interesting. rather than present the tools seperately, the exercises evolve to mimic the drawing of a building from A to Z, mimicing the process that occurs in an atelier.  I think battling your way through Revit without an expert might lead to losing a lot of time and picking up inefficient habits on the way.

It is in french though of course; if that is an issue, perhaps someone can suggest a similar course in English.