yes as jim says, no need to worry, it'll be toast long before it stops spinning. in around 4bn years the sun will expand to a red giant possibly as far as the earth's orbit, though the jury is out on that at the moment. Regardless, it will be close enough to boil off the atmosphere and oceans and melt what's left into a giant snooker ball of molten rock. Something to look forward too!
Earth's rotation slow because the tides transfer energy to the Moon raising it to a higher orbit. Eventually the Moon and Earth would become locked so that the month and the day were the same length. The Moon and Earth would face each other always with the same sides.
However, as others have pointed out, the Sun will have burnt Earth to a crisp before enough time had passed for the Earth and Moon to rotate as one.
Life as we know it will have perished much earlier. The oceans will have boiled away within about a billion years because the Sun is slowly growing hotter.
Hopefully the brightest and best will have left to colonize new worlds before then. But sadly it is more likely to be the rich and politicians who are on the first flights out
thing is.. when all the politicians live on their own.. Who will sort their politics? It won't be an all involved thing.. a select few will run the others and boom..
We need to take a leaf out of the Golgafrincham's book but send Arks A and C off in a different direction from the rest of us when we finally leave the planet; making sure we have a healthy quota of Telephone Sanitisers first, of course. :o)