Payton has built the team he wants and has it ready to win a Super Bowl right now. There is 0 percent chance he walks while Brees is still playing at a high level. Even if Brees was to get injured / decline / retire, I bet he would rather try his luck with a new QB instead of searching for greener pastures.
JJ could write him as big of a check as he wants, but Payton would likely turn down even a Jon Gruden level payday - per Google, he's already making $8 million a year, and even doubling that probably wouldn't be life-changing money for him. The only way I think you could bait him out financially is if you offered some percentage ownership of the team.