Expect it. Every GM will make the saints pay a kings random for a trade up. And the Saints will expect it as well.
The only thing that would help, is if Garret Nussemier told every other team that if they draft him, he will refuse a second contract. This would force a team to consider if 5 years plus a franchise tag year or two is worth it.
If I had to guess, I would guess we will be picking somewhere between 17 and 22. I would expect to lose 2 or 3 first round picks as well as a couple of 2nd round picks and maybe even some 3rds.