BioWare has begun testing high population servers, beginning with those who had characters on east coast servers. The company announced that all east coast characters were copied over to a public test server, and is encouraging players from the east coast to log in with it to test it out.
A blog post walks through the steps to join the test server, and notes that customer support isn't offered for it. Instead, you'll need to hit up the test forum to give feedback if anything is broken. It promises that by the time the server switch is over, it will provide a better experience with significantly increased population.
BioWare didn't mention how few servers will remain once consolidation is complete, but it did say that eventually origin servers will be closed and players will be redirected to the new destination servers.
This is likely a move to prepare for the game's free-to-play transition, though it may also be a response to servers being more sparsely populated these days. The developer recently announced it would be aiming for an update every six weeks to keep fans interested for the foreseeable future.