I have never had to write a large proposal but I have been involved in going over proposals for dollar amounts ranging from $100k to $1M. I am not sure where this budget comes into play. But it does play an important part of how much effort you are going to put into it.
Budgets of $10k to $100k don't require as much work. But if you really want to job you put more into it.
The basic idea for the proposal is to bang on cover everything they are asking for in as clear a maner as possible. In all the RFP's I have looked at you will have a "requirements" section which is a numbered or bulletted list of items that they want. If you can not meet all of these requirements you might be in trouble. Sometimes the requirements will be a little faulty. They might request something that just doesn't work, or works different than they describe this. Make sure to cover these as best you can.
You will often be asked to number of rate how well you can comply with their requirements, come as close to perfect as you can. Don't lie, you'll just be screwing yourself. I like seeing almost a copy of what I have sent to them with the rating on it. Then in a later section explain all of your claims.
For example they might request something like:
Create a content management system for class scheduling.
You would rank your ability to do this, in one section which contains only their requirements, and in the following section you would breifly explain how you that you can meet this requirement exactly or you can come close to meeting it and how your solutions would be different.
You will want to cover payment similar to how you cover payment for any other contract 50% or more down payment 25% at 50% complete landmark and balance at completion. You will want clauses about revisions (the great CSS site with the fish on a cutting block has great stuff about revisions, I can't remember the name). Ass saving basically comes down to you collecting the money, requiring their approval, requiring their content packs, and having them sign off every step of the way. If they go back there is a penalty (paid then and there), you want no room for project bloat. You will really want an easy to read project timeline. Visio tends to be the standard tool for this, and it is really ugly most times. Make sure it is readable to people who have no knowledge of anything computers. Actually make sure everything is readable to people with little or no computer knowledge. The people who wrote the RFP might have a good idea about what is needed, those who control the money might and probably do not.
Also, and RFP is not all about giving them free design options, nor free database diagrams or the like. Those are delivered when they have signed a contract with you for you to preform the work. You don't want to really get dicked by giving them that stuff.
Since this is web design you will not have to worry about such things as source code eshcrows which is very nice. You might have insurance issues, they would be in the RFP. I am not sure if they would require you to have liability insurance, sometimes you are required to have that. If not that is good for you.
With large projects it is often important to put in what you do charge per hour. Most of the proposals I deal with have rates of $150 per hour for programmers (read applications programmer). I think it is ridiculous but that is what they charge. But those rates are normally for items such as additional labor after you have delivered the final project.
I ranted a whole lot, which I thought might give you some idea as to what the basic idea I delt with it. I think some highlights might work well.
1. Price is very important!!! If you are the lowest price providing the necessary services you have a good shot.
2. If you do not meet all of there requirements you might be in big trouble.
3. If your Proposal is not easily read by those who are not computer literate you might have problems. Don't dumb it down, but don't make it more technical than it has to be.
4. You proposal is there to get you in the door. What you are really trying to do is get a meeting with them. So you can talk to them.
5. Do your homework. Use every resource available to you. If you have knowledge of logos or things they would be using, or terminology they like to use, or other things that show them you have done your homework it makes you look good. I had a company who designed a mock up applicationed tailored for the department I worked with logos and the like and it made an impact on a lot of the people.
Finally. Take all this with a grain of salt. I don't know anything about what you are dealing with so I could be completely off base. My experience comes from the other side of the table, and in dealing with RMS systems and nothing to do with web design.
If you have specific questions I might be able to field them better. Congradulations on the client! I hope you do well with your negotiations.