Hey John,
I'm going to try to go through all of your answers, one by one:
1. Can it hurt us to blog at a high volume (4 blogs per day) in an effort to include all of our keywords and attach them to state and city specific keywords (ie. "keyword one" with "keyword one city" and "keyword one different city")?
Yes, if the articles end up too short or too similar. 4 posts per day isn't necessarily a bad pace, it's just the quality of the writing that can get you into trouble.
I don't know what your service is, but, do you need to have a variation for every city? I work for a business that provides city-specific services, but we write blog posts that are relevant for the whole nation, then have pages describing what we offer for each city. We do have some location-specific content, but most of our blog posts are not.
Here's the way I'd figure it out: when people are looking for a given keyword, do they usually use the city name? When you search for the keyword without the city name, does Google return map results? If the answers are no, you can write one article that isn't location specific, and Google will rank it in all locations.
**2. Is it more valuable to blog only a couple of times per month with deeper content, or more times per month with thinner connect but more keyword involvement? **
Totally depends on your industry. And company. Deeper content can rank for more keywords and has a better chance of getting inbound links, but it can limit the keywords you target. You really need to think about ... (next question) ...
3. Our customers are forced to use our type of product by the government. We are one of the vendors that provide this service. Because of this our customers may not care at all about anything we would blog about. Do we blog for them, or do we blog for the keyword and try and reach partners and others who would read the content and hope that it also ranks us high when our potential customers search?
You should write content that appeals to whoever makes the decision to use your product.
How often does the government choose whether or not to provide your service? If there's any chance at all that you could eventually lose your contract, write content that appeals to the people who choose vendors. How can you make their decision to work with you easier? Write articles about how your service solves their problem easily. Interview some government officials. Make it clear that you understand them. Also, write about whatever your company is knowledgeable in, so it's clear that you're the thought leader in your space.
If it's really unlikely that you'll lose your government contract, or the government track doesn't work, I'd just focus on the last part: what knowledge does your company have that others don't? OKCupid, for example, got great links through their blog, which showed in depth analysis of how we date (making it a great purchase for Match.com, who, alas, stopped blogging). Pinterest developers have a Tumblr called Pingineering that talks about how their engineering team tackles big data issues (granted, this isn't on their site, but they're not struggling for links or rankings).
4. Is there an advantage/disadvantage or does it matter if we have multiple blog authors?
Nope. Go for it.
Hope this helps! I wasn't able to be very specific without knowing your specific industry, but this should point you in the right direction.
Let me know if you have any questions!
Kristina