Learning the song has nothing to do with tempo, that is a performance issue (rehearsal).
If you have learned the song you can play play all parts of it, if you struggle with a part then you have not truely learned it.
Check out the link, this is truely learned as they required no-one when they pracatice it. http://youtu.be/J-ZdmlKX06A
You will find that when you learn a song, that is the mental part, the playing of it is a performance, that is the physical part. It os common for player to learn a song, and struggle to play it...then wake up one day and find they can play it. All that has happened is the physical side has caught up with the mental side.
When you first pick up a bass it is 100% physical 0% mental, because you cannot play what is in your head.
As you progress as a player that ratio changes it becomes 90% physical 10% mental, then 70% physical 30% mental etc.
This procces continues, till you hear a song and can play the song as a performance after just hearing it a few times...your brain will order the notes and your brain will relate that info to your hands. This is what is happening from the very start, but now your brain and hands are becoming one, so the time between learning and playing is getting less.
A rut or dead end is when the physical side leads the brain. Easy way out is to learn new ideas and have the physical side follow the brain again.
One last point, if i tried to explain this post in Russian, but could not, that does not mean i do not know what i am talking about, it just means i cannot physically do it, but i still have the knowledge of what i want to say, i have still learned my subject, my facts etc.....but i just cannot explain that in Russian.....so the two are separate things....just like learning a song and performing a song are two separate things. But the more they are used the easier it becomes..a dis-jointed song becomes a flowing song and broken Russian speech become fluent Russian speech.