We were just there yesterday morning.
It was our last day in Rome and we only had the morning before we flew out. We arrived by metro to the Basilica around 7:30. Walking down the street from the metro the line looked quite large (although much smaller and less crowds around it for earlier in the week when we came over after the Vatican).
The line moved quite quickly and took about 10 to 15 minutes. This was the line for security.
We went through no problem. You kind of have to be assertive and get your way through. It isn't a nice single or double file line, but a mob that gets sorted towards two security areas and then sorted into security lines but even those were often two lines merging. The tour guides have no problems shuffling their groups through so hold your ground! (It isn't aggressive but if you are passive the line in front of you will continue to grow).

Go early morning and you'll have no problem.
If we didnt have our two boys there with us I would have been in line at 7.

From when we got in the Basilica to when we got out the crowds were still small but you could notice a difference.