I love learning songs, as do a lot of people that I know, including many of my students. It's a big deal though for some people who do it for the first time. As with most things, the more that you do it the easier it will become but if you are a beginner it can be really daunting and can sometimes feel that you are going nowhere fast with frustration rapidly overtaking enjoyment.
The first time I went out and tried to learn my first 'proper' song was when I was 13 and had been playing for a few months. Me and a mate went to the local music shop to buy songbooks that we were definitely going to master. He chose Iron Maiden, I chose Jimi Hendrix.
Awesome. I got home and started on the first tune in the book, 'The Wind Cries Mary' which is a great introduction to playing Jimi's music but for someone who had been playing for barely 2 months it may have been overly optimistic. I started at the beginning of the tune, reading the tab and following the song through. 45 minutes later I reached the end, non the wiser to anything that I'd done. I'd played the song (in a way) but not much else.
What would have been a much better thing to do would have been to use that 45 minutes to learn the classic introduction to that tune. Then at the end of it I would have actually had something that sounded vaguely musical. Instead I wasted my time and was left puzzled why I wasn't playing like my idol.
Clearly I learned a lot about what not to do and I use this story when students are learning songs, whatever the level that they are at. In my opinion it's better to get once small piece of the music right, played cleanly, in time though not necessarily at the full speed of the piece, articulated well and with a nice tone. However this can be a very long process, especially if the song is long so students have to perceive and be prepared to put a lot of work in and not expect big results on the back of small amounts of practice time. Even if the student doesn't have hours and hours between lessons to practice they can learn far more about playing guitar from just getting a small piece of the song sounding good and over time build up to learning the rest. Otherwise all that happens is that they end up with a substandard piece of music and a lot of bad habits that need fixing.
Patience is key and also learning the right tunes so that you aren't over-faced too soon. 'The Wind Cries Mary' is a great tune to learn if you want to be able to play 'Castles Made Of Sand' as many of the techniques found in 'Castles...' have their founding in the simpler riffs of 'The Wind Cries Mary'. However, if 'The Wind Cries Mary' is too hard you will need to either develop the patience to continue with it or spend the time learning simpler tunes and studying the techniques required to help you learn and play what you want to.
As for me, I've gone with the first option and have been learning 'Fuzz Universe' by Paul Gilbert since September (it's now February). I have about a third of it up to about 60% speed and my patience has never been tested as much! Wish me luck.