There are a couple of things I would think would work. One is to take it out a wash it off and wrap in cheese cloth if you want to smoke tomorrow
The other is the bring it out of the brine and hit it with some rub and wrap it up real good to keep it from drying out
Too much brine can affect it but not knowing your mixture it is hard to say
What he said^^^^^ After all he's the person that came up with it. I have used it this year but I never brine for more then overnight. There's isn't that much salt in it but I would still take it out of the brine and put it back in the refrig and leave it there till you are ready to smoke it.
The last bird I did I ended up brining it for two days by accident because things came up and I had to put the smoke off till the next day. It was excellent so I started my birds in the brine at 4:00 in the am after I got home from work. I only used a quarter cup of Kosher salt because the birds already had some salt solution. Hope I didn't screw up starting too early.