These forks are generally not based on a date, but rather a block number where the change in specification begins to be applied.
I am reading the block number that has been coded for the fork is 494,784. So it would then be the first divergent block (that would be accepted as valid by SegWit2x nodes but rejected by non-SegWit2x nodes) added to the blockchain on or after that block. Block number as of the time I'm writing this post is 487,281 and there are on average 6 blocks created per hour. So, about 52 days from now, which would be November 18-19.
One thing about this upcoming fork that people need to clearly understand is that one of the parties that is forking the code off from the Core bitcoin code is not taking steps to implement "replay protection". Simply put, this could cause any value stored on the split chain (the side that is forked away from Core) to be able to be spent by others. I do not believe there is a danger to the value on the Core blockchain, but if I am mistaken please correct me.
Any time a split like this happens, it's probably a good idea to move any funds you have into fresh wallets on both chains. This must be done after the split has been completed -- doing it before will not protect your funds.
Again, if I am incorrect in anything I just stated about the consequences for stored value due to a completed fork, please correct me as I am just trying to explain things as I understand them and do not want to contribute to FUD if I am mistaken.