What does "jackpot" mean in this passage?
Solution 1:
This is an example of meaning #1, but "some jackpot" is being said sarcastically. If the potential payoff of the shot were a complete cure, that would indeed be a jackpot, but instead they're saying that chemotherapy, which is a very difficult and dangerous process, is potentially the good news here. Chemotherapy doesn't really seem like something to celebrate, so the speaker says, sarcastically, "Some jackpot."
It would be easier to understand if you could hear the speaker's tone of voice when he says it, but another clue is when the other speaker says, "the good news—the good news—is that I get to have chemotherapy." The repetition of the phrase "the good news" emphasizes that this phrase is being used in an unexpected way, to introduce something that isn't necessarily good.
Solution 2:
@Nicholas' answer is correct, but I thought I would add some information about the word "jackpot" itself, as the dictionaries I looked at didn't really seem to include this information.
The most common truly denotative use of "jackpot" refers to a large single win at gambling, frequently one that is solely luck based, like from a slot machine or lottery. You wouldn't generally use it when the payoff is small or if it were won over multiple transactions, even if it were large. (Incidentally, "to hit the jackpot" is a commonly used phrase meaning "to win the jackpot".)
However, it is often used metaphorically, to the point that it has become a standard definition of its own. But I think that it still needs an understanding of the gambling-based definition in order to really understand its usage.
In this case, it is definitely being used sarcastically.
"Some jackpot."
"That's some jackpot."
"That's an excellent jackpot."
"That's an excellent large and unexpected reward."
By the way, in spoken English, "some" would be strongly emphasized in this usage, and is probably more frequently used sarcastically than not.
(By the way, the gambling usage probably stems from card games where a pair of jacks is required to play, but blind antes are required regardless of whether or not the person paying the ante will play the hand. This leads to a situation where the pot may build up with blind antes before anyone has a chance to play at all.)