@Laura H., a couple things.
1) If you have realized gains on those investments then you're going to pay a capital gains tax when you sell. So yeah, the tax man will come calling but if you time your sell you can pay those taxes in tax year 2016. I don't carry credit card debt but if I did I would make it a point to pay that off before even thinking about investing, but that's me.
2) Your oh sh*t fund isn't exactly what I would consider an oh sh*t fund. I want my emergency fund more liquid than what stocks can offer. What happens if you need that money when the markets are closed? If you need to get to it quickly you might not be in a position to do so.
3) Others have stated using the money that you're currently putting into your 401k and putting it towards your credit card debt. That sounds like a good plan as well. You have some options here. Balance transfer, selling stocks, rerouting your 401k money etc. I'm sure there are others that we haven't hit on yet too.
Good luck!