I was directly involved in the current AF1 aircraft - and I know that Boeing lost hundreds of millions on those two 747s due to the fixed price nature of the contracts combined with less than elegant program management.
Shortly before I retired from Boeing last October, I was given a briefing on the upcoming replacement and how it was going to affect the engine package.
While nearly everything is proprietary/confidential (meaning I can't talk about it), I was quite frankly shocked at the level of 'gold plating' that was going into the requirements with little - if any - regard to the associated costs. Right now, it's looking very much like another 'cost is no object' program. $4 Billion doesn't sound out of line for what's being asked.
If nothing else, I think the USAF needs to go back and scrub the requirements with an eye on cost vs. benefit.