Adam,
Upon reading your more detailed description, I would offer the following advice:
Firmware, or embedded software, is an interesting conecpt these days. There are as many compilers as there are chips just about. I worked on a project that used firmware (to which I communicated serially) on a TI DSP. The firmware had a custom compiler designed for the chip (marketing has a LOT more say than engineering or just plain common sense these days, and it seems that TI is not exempt from the whole "let's do like Microsoft and make everything product specific so they have to buy everything from us") So, in order to really answer the question, you have to know what type of firmware host you are dealing with.
Look at the documentation for the chip. Find out what type (if any) operating system is on the chip. The easy answer is if it is embedded Linux. Then, you are set, and don't have to learn C. However, I suspect that the opsys is not generic, and you will be forced to learn C. Take a class at your local community college, or better yet, make the company pay for an advanced training 'crash course' offered by some training organization or college extension.
However; if it is a generic opsys, or one supported by LabVIEW RT or similar, then you are in luck, if you want realtime.
Spend some time looking into the problem. You may like the answer, you may not. Either way, I think you have a golden opportunity. The embedded market in moving quickly.
I am glad you are asking this question. LabVIEW needs to make a definite move into embedded systems. Richard Jennings (Gary Johnson's co-author) gave an astounding presentation on embedded LabVIEW at NIWeek this year. You should order Gary Johnson's latest book (McGraw Hill - Power Programming 3e, Gary Johnson and Richard Jennings), he included a discussion on this very topic, and even included step by step instructions and software needed on a included with the book.
Good luck, and be sure to let us know what you find out.