Well, the song was transmitted 218 days ago. Traveling at the speed of light, the song has covered a distance of 0.59 light years or 3.5×1012 miles - that's 3.5 trillion or 3,500,000,000,000 miles.
That's a long way, huh?
Across Not Very Much
Actually, in cosmic distances, that's barely the end of the garden path in our own back yard.
The nearest star, Proxima Centauri is over 4 light years away. "Across The Universe" hasn't come across anything! It's only traveled 1/8 of the distance to our nearest star (but the signal doesn't even go in that direction anyway, so the Proxima Centaurians won't ever be dancing to Ringo's beat).
Nobody said communicating across the Universe was easy, let alone fast! We can forget about using this Beatles song as a means to get the attention of any alien civilization for at least 400 years (although Polaris isn't really an alien-hunting candidate anyway). No, this was just a symbolic message... to no one in particular.
However, within the next few months, the Oort Cloud (the hypothetical volume of space surrounding our Solar System, approximately 1 light year away) will soon be echoing with the Beatles... but there's nothing there to receive the radio signal anyway, just a few icy proto-comets. Oh well.