Again, it does NOT matter whether it is you or him do the talking, the offers are in the system and the offers do change over time. A good fishing trip would be able to get the reps dig deeper to exhaust all the offers already attached to the account.

If you are not satisfied with the offer you could always say, Let's think about it then thank the rep and hang up, Call another day, another week - new offers may show up and more to your liking. For example, 3 weeks ago a friend called for her bold - there was nothing. Without tried again in a week or two later, she canceled her card. Now you see 10K bonus for $5K spend or outright waive the $95 are not uncommon. All she needed to do is a bit more patience as the AF was not due till 3 weeks later. Besides she could always get the AF back within 60 days should she decided to cancel after all.

It is always a gamble and the information posted on this thread is always helpful to learn about what offers are out there. I would say to have patience, and a PLAN as to when to start calling. Call one to two months before the AF is billed. Good if there is positive outcome. Else, call again a few weeks later. Call again after AF billed... You get the drift.