If I apply over 6v to a high speed cmos chip, (specifically the 74HC4060) could it short my circuit, and make the battery I am using to power the circuit feel hot to the touch?
That might not be the problem... How much over 6V?
Do you have a multimeter? If so, you can measure the resistance of the chip between 5V and ground to check if it's shorted. Usually, if the chip is burned-out, the chip itself will overheat.
With these inexpensive parts, it's always a good idea to buy a couple extra chips. And, if it's in a socket, it's easy to try another one...
Where I work, I've accidently connected 12V to a 5V board several times. :( Usually, the RAM chip burns-out, and a few times the CPU has burned-out. (The RAM is soldered-in, but thankfully the CPU is in a socket.) But, the regular 74xx logic chips never seem to burn out at 12V.
Another board I test has a voltage regulator on board. I always run 6 - 6.5V into the board to test the regulator. When the regulator is bad, or if the regulator-bypass jumper is installed wrong and 6V gets applied to all of the chips, nothing bad happens. (That's why I run it at 6V... I need to feed-in more than 5.5V to test the regulator, but I want to keep the voltage at a safe level...)