You've never had to have cash on hand. $200+ in the bank is all you ever needed.
The quest isn't explained that well in-game and the steps are out of order and incomplete on the WestStats... this is not a secret quest so I'm not divulging state secrets here...
Highlight the text below if you want a walk thru on the entire quest:
First part of the quest you have to be doing nothing at 7pm in-game time and have 200$ EXACTLY on you and have NO weapon.
After 7pm - click on the saloon and look for a new quest from the Sheriff.
You have 20 minutes to defeat the Thief in a duel with NO weapon. He is very easy and does very little damage, so you can try many times until you complete it if needed.
You get 1200$ and 600 XP for completing that part of the quest.
Then you need (5) Silver from Silver Mining.
After you have 5 silver you have to wait until Wednesday ... then remove your weapon and check the Saloon for the "Defeat Dealer" Quest which is pretty easy.
Note that you must keep the 5 Silver until after you Defeat the Dealer, and I don't know if it can be anytime on Wednesday (I think) or if you should just keep looking for the quest randomly during the day. (It showed up for me minutes after midnight in-game time.)
You get Kates Ring from the Dealer and can then turn in the quest to get +2 Charisma or +2 Strength - you have to choose.