If you just want to contract with them, it is easy and you are just a contractor. If you want to be a vendor then below is my experience & opinion.
We have been successful in breaking into the EMS/Fire and more limited in Law, but it took a long time and also I do have contacts in the industries.
As MalcolmDiggs already pointed out, most times these deals are awarded to the lowest bidder and take time, 6-12 month sales cycles are not abnormal, 3 months is considered quick. Additionally the RFP is usually a multistage process, not just submitting a quote and response. Many times you have to appear at minimum to one Q&A session, plus submit your RFP and prove your bonafides. Depending on the agency as well, if the value exceeds $5k or $10k (or whatever their threshold is) then you will have to be bonded, prove you carry all the proper insurance for the state, blah blah blah.
Where this can get a little easier is if you have developed a product that one of the agencies wants to acquire then it is usually a longer sales cycle but you get out of the RFP process a lot of times. They will sole source things, or many times write the RFP/RFQ so specialized that only one product fits it.
In general though, once you get 1-2 of these deals they are easier to get, because there is a certain amount of the safety in the fact you have been trusted before so the next time it gets easier.
Our last Response to an RFP took us the better part of 30 days and 2 people (over 3 months) to properly write, assemble, document, respond to Q&A and get everything sent in. Plus we had to provide financials, resumes of principles, bond, proof of all relevant insurances etc. Luckily since we have done these before a lot of that is just refreshing documents but it still takes time to make sure it is all in order. One we responded to claimed to have rejected our proposal because we put two sections out of order in our response, a stupid mistake that didn't materially change anything, but it wasn't in the specific stapled order they required.
Follow up question: what is it like building products for acquisition by such organizations? Is this anything like building B2B or B2C enterprise software? What common requirements do orgs put on software or services they want to acquire?
From our experience building products is much like building for enterprise companies. The sales cycle is still longer than private businesses but it is better than trying to win custom work through RFP's usually.
They will still require some additional vetting usually, like we have had to provide financials a couple of times for larger product sales > $25k so that the County could feel good that we were a solid company and not going out of business the next week. But we even got a deal where we had horrid financials (in the red), we just explained we were still investing in product development etc. Sometimes I think it is more about them checking boxes than someone really evaluating all the points.
It is also not uncommon for them to ask for the software (even a SaaS) to be put into source code escrow so that upon any insolvency (or other triggers) they get a copy of the code. And while you have to arrange it, they all pay for it and pay for the extra time it takes you to manage that process so it isn't a big deal.
Lastly, pricing is really key on these types of products and services. If you can get within credit card purchasing limits for a product or service then the approval process is just getting someone with the card to say yes. For example, say you have a service for $39 a month, that is well within the purchasing card limits monthly for most small County departments. One time purchases are generally set around 249, 499, 999, 2499 because you will find the managers will have a purchase authority up to $250, $500 etc, where it doesn't require any review. This is really the key on how to sell into them without having to be vetted or go through an RFP etc.
We have been successful in breaking into the EMS/Fire and more limited in Law, but it took a long time and also I do have contacts in the industries.
As MalcolmDiggs already pointed out, most times these deals are awarded to the lowest bidder and take time, 6-12 month sales cycles are not abnormal, 3 months is considered quick. Additionally the RFP is usually a multistage process, not just submitting a quote and response. Many times you have to appear at minimum to one Q&A session, plus submit your RFP and prove your bonafides. Depending on the agency as well, if the value exceeds $5k or $10k (or whatever their threshold is) then you will have to be bonded, prove you carry all the proper insurance for the state, blah blah blah.
Where this can get a little easier is if you have developed a product that one of the agencies wants to acquire then it is usually a longer sales cycle but you get out of the RFP process a lot of times. They will sole source things, or many times write the RFP/RFQ so specialized that only one product fits it.
In general though, once you get 1-2 of these deals they are easier to get, because there is a certain amount of the safety in the fact you have been trusted before so the next time it gets easier.
Our last Response to an RFP took us the better part of 30 days and 2 people (over 3 months) to properly write, assemble, document, respond to Q&A and get everything sent in. Plus we had to provide financials, resumes of principles, bond, proof of all relevant insurances etc. Luckily since we have done these before a lot of that is just refreshing documents but it still takes time to make sure it is all in order. One we responded to claimed to have rejected our proposal because we put two sections out of order in our response, a stupid mistake that didn't materially change anything, but it wasn't in the specific stapled order they required.