If he's that wealthy, he probably already has the contacts in place to buy or lease a jet fairly quickly.
I used to work for an airplane broker. He dealt only in smaller jets, not planes that would be bought by airlines or the like. He had some deals that took a few weeks to a month, but that was usually with a lot of haggling going back and forth and nitpicky changes to the contract. But if the guy's desperate, it could happen a LOT faster.
The broker would usually make all the arrangements - like flying the plane to the buyer's destination, providing the buyer with all the service history on the plane, and arranging a test flight.
It's true what everyone upthread is saying - those rich people who buy jets want their jets decked out their own way, and that takes time and money.
But yes, it can be done in a day provided the guy is reasonable about contract issues and is willing to pay whatever it takes. Used is easier to buy than new since new usually has a waiting list of a few years, especially for Gulfstream IVs back in the day. Not sure about now.