Seems like common consensus is to stick with the .jar launcher until this bug is resolved.
Also having this issue, where the update stalls at 59.90 MB.
This may be a pretty recent bug, but it's a definite problem if people that want to run Minecraft can't even get the launcher to load.
Found the source of the problem!
In Avast, you'll need to disable both the File and Web Shields found under Preferences > Shields. Once both shields are disabled, you should be able to get the newest version of the launcher.