Apologies for brevity (posting from a plane):
Small businesses can absolutely get government contracts, but becoming very adept at doing this is a skill, comparable in execution difficulty to, I don't know, SEO or cold calling. There exist many businesses in your town which, month in and month out, respond to RFPs for government services in the five figure or six figure range.
If there is any interest, I'll share Appointment Reminder's (unsuccessful) bid for a government contract in Hawaii. That's not ordinarily a huge portion of our business, but I became aware of the opportunity and it felt like a lay-up. It wasn't, as I failed to discover a key piece of information (namely, that an enterprise competitor had won the contract the year prior on a bid that was half of the minimum that I'd contemplate), but the process was not extraordinarily oppressive by the standards of An Adult Who Occasionally Plays Like This Is A Real Business.
Long story short: the white-hot competition to deliver 100k phone calls a year produced exactly two responsive bids, for $30k and $15k. The competitor, who won, won with a one-pager that said "Details substantially same as last year; if you don't have our old brochure on file let me know and I'll re-fax. Signed, an employee whose only job is to file 250 bids for $15k a year and probably gets a gift certificate if more than 50 turn into sales."
My model for that bid, by the way, was "$5k of AR services, $10k budget for extra Twilio calls, $10k for software customization, $5k for anticipated hassle." That's an internal model: Hawaii only cared about the final number. (I can buy my competitor having economics which made their bid profitable at $15k, particularly if they amortize engineering costs over multiple years of anticipated renewals and/or they do enough similar business to amortize customizations over multiple accounts.)
The cost of the process for us:
Two hours of reading accessible online documentation of vendor qualification requirements for Hawaii, written at a 5th grade reading level.
One hour to understand the bid requirements.
Four hours writing a proposal which, like all proposals responsive to government RFPs, is basically "The system will be capable of Copy Paste Language From RFP Here. One sentence of elaboration."
Two hours of pushing faxes around to supplement the data collected by Hawaii's (fairly painless!) online vendor qualification process.
One hour responding to a general excise tax audit occasioned by a filing of Hawaii state business registration mandated by the process. (Result: we do not owe it, as anticipated.)
$60 in out-of-pocket costs for various regulatory fees.
Plenty of companies do this stuff week in and week out, for everything from "dig up a military statue and transport and replant it to a new location without causing structural damage; $40k" to "400 orange jumpsuits; must not contain any structural element capable of causing suffocation; remove all elastic; shipping included; $8k." It's like any other sales process: you win some, you lose some, you build processes such that your win rate costs you a percentage low enough to allow you to still make money on the business.