The plan was not for the Department of Defense to have an additional Orbiter built for it. Instead, the Orbiter Discovery (OV-103) was to be dedicated for DOD use and based at the Vandenberg launch site. (Space Shuttle, Dennis Jenkins, 1992 edition, page 151)
Prior to the Challenger accident, when NASA was preparing to
launch the space shuttle from Vandenberg AFB, OV-103 was the
dedicated vehicle for the Air Force. Because of this, she had a
different TPS design.
Reentries coming into Vandenberg . . .
had a higher cross range requirement, meaning as you’re
descending you had to come off of your normal inclination and turn
into Vandenberg at a much farther distance from your normal
trajectory, which means you had to put it down steeper and you’re
getting higher heat loads. So it had a different TPS design on the
underbelly of the vehicle.
SPACE TRANSPORTATION SYSTEM HAER No. TX-116
Quote is from Bill Roberts interview at the JSC Oral History page.
To address "how far did it get" the plans for the first Discovery mission out of Vandenberg (STS-62A) were well along. We had started building training loads in the Shuttle Mission Simulator for the mission, I myself flew launches out of Vandenberg in the simulator. This means that the flight software had been processed and configured for the West Coast launch prior to its incorporation in the training load.
It would have been the seventh mission of OV-103. Her third mission, STS-51C, was a dedicated Air Force mission.
This crew assignment sheet from September 1985 shows 62-A on the manifest. Flights from Vandenberg, using the confusing naming convention of that time, were to have a "2" as the final number digit of the flight number. A second Vandenberg launch, 62-B, is shown, but had no crew assigned yet.
When this list was produced, STS-51I had flown, and STS-51J was next up. So 62-A was seven flights in the future. I personally felt the chances of that happening as scheduled were slim - there was a lot to be done, especially the qualification of the Filament Wound Case (FWC) Solid Rocket Boosters (SRBs) planned for Vandenberg launches. (FWC SRBs are mentioned in this paper Space Shuttle Solid Rocket Booster Lightweight Recovery System) Wikipedia gives 15 July 1986 as the planned launch date, but does not say as of when.
(Source - personal collection)