Should I tackle the CC first before I focus on saving?
Unless you have an insanely low special interest rate the answer is absolutely yes, no matter how long it takes to pay it off.
If you have an open credit line then that can be your emergency fund. If an emergency happens and you simply have to pay for something, that's a valid use of the card. Until you have it paid off there's no need for an emergency fund, and your return on investment from paying off a card dwarfs just about anything else.
That said, if you actually do have an insanely low rate (0% APR for 12 month offers and the like) you may not need to pay it so quickly, just make sure you can when the teaser period runs out.