Here is the last thing I saw before the command prompt:
Searching for binary rubies, this might take some time.
Found remote file https://rvm.io/binaries/osx/10.9/x86_64/ruby-2.1.1.tar.bz2
Checking requirements for osx.
About to install Homebrew, press `Enter` for default installation in `/usr/local`,
type new path if you wish custom Homebrew installation (the path needs to be writable for user)
: Requirements installation failed with status: 1.
I don't think it made it to the point that I could press Enter
If anyone else encounters this particular "status: 1" error (I know a number of people have received this, but it seems for different reasons)... I can confirm depa's comment and will add to it to create an answer to the question:
I just had to install Homebrew myself using the command from brew.sh:
ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
Then when I ran the RVM install command again it worked fine.
It seems RVM had a problem installing Homebrew on my machine for some reason.