There are ways to purchase government fares without a government credit card. The most common way that I know of entails the use of paperwork known as an Official Travel Authorization (OTA). This is given to the government travel agency issuing the ticket. What happens to the form after that, I am unsure.

But I would echo the comments above that use of these fares is strictly controlled. Misuse would likely cost someone their job.

The government fares that I saw during my time with the federal government were, like letiole said above, significantly higher than the lowest advanced purchase fare on most major carriers yet cheaper than a walkup fare.

Average examples that I can remember were roundtrip government fares between DCA-BNA and DCA-MEM usually running close to $600 (refundable, no-Saturday night stay), whereas lowest advance purchase fares on these routes usually runs about $250 roundtrip (w/ Saturday night stay).