Armory takes 8 Hours to sync. Is it going to get worse as Bitcoin becomes more popular? I have been experimenting with Bitcoin and I installed Armory wallet. It told me that it would take approximately 8 hours to sync the worldwide ledger.

My question is, as Bitcoin gets more popular, will it take longer to download the ledger?

If so, doesn't this pose a problem - could it get to big to be feasible?
The short answer would be yes, if the chain 
becomes bigger it takes more time to download
it.

The more detailed answer would be: there is 
plenty of options to make it quicker: for
example you can download already constructed
chain from some trusted source.