I got a big federal contract at a company I used to work for and had no ins at all. It was an IDIQ, indefinite quantity, indefinite delivery that was capped around $2mil a year. It was a sole source for multiple items and nobody that bid on it caught it. I went higher on the stuff that they would use in quantity and lower on the oddball stuff that I wagered they would not use which put us as low bid in total but with higher pricing on the good stuff.
I have also bid a lot of local municipal contracts, those I did not care for one bit. They line item each thing so the pricing is all in the toilet and they dictate the terms of how you do business. What solventinkjet said is also true, if they want a specific vendor or product, they will make it work through the bid spec. They also usually have a convenience clause which gives them an out when they decide that they don't like you or they want to help out their buddy.
The good thing on some of them is they may bid out 18x24 parking signs where you drop your pants on those and then usually pick up a lot of other non-bid work where you can make your money back but that can be a gamble as well.