A "shotgun approach" is a very normal style request from the GSA. If an integrator wants to be a part of the GSA, they better have a specific person who is educated on GSA and handles all GSA things. As a contractor, you really need to be educated if you want to be a part of the Multiple Awards Schedules Program. Not just education, but have a lot of time to work on GSA things and also relationships with other GSA contractors.
If you look at the companys who get the most government awards, their main core of business is with the GSA, hence why you see similar company names on a yearly basis for $ amounts.
This is why you see these 3rd party companies (Contractor/Agents) in the market because they thrive by the ability to navigate through the GSA.
An Integrator with no GSA skill could have a hard time to even know what Schedule's they should be a part of as there are more than 1 schedule for similar types of trade skills/products. Even if an integrator took the GSA classes, it is still a challenge.
Back to your question. A majority of GSA quote requests are shotgun style approaches. If you cannot navigate through the GSA weeds, you will be out of luck with your shot gun style "offer" you sent in.
this is the first time we've received something from the US Government
Did the 'shotgun' quote come by USPO or in an e-mail 'blast'? For your eyes only? :)