Has many possible meanings. Firstly though it's a line from the Smashing Pumpkins
off the Mellon Collie and the Infinite Sadness
One thing I think it means is that tomorrow is not very far away at all. In fact it's just an excuse away and an excuse is something that is very easy to come up with. So if you need something done, say an assignment or study for a test and it needs to be done before tomorrow, then that's not much time at all to do it. Tomorrow is just around the corner so if we don't do something now, it's going to come and it will be too late do anything about it.
Also can be seen the other way, you might want tomorrow to come. For instance you might be with a lady friend and want to stay the night, and thus see her tomorrow. You might have to work in the morning or, have something important to do, but tomorrow's just an excuse away and a simple excuse can get you out of those things and into a night of passion.
If you drop the away then the meaning is changed completely. Instead of tomorrow being what an excuse is made up for, it becomes the excuse. Saying to someone "tomorrow's just an excuse" is like accusing them of putting something off, of avoiding an issue, a task or a problem. By going "I'll do it tomorrow." or something like that all you are doing is making an excuse not to do it now. Tomorrow becomes the excuse to people who believe that there is always going to be enough time to do everything that they want to do, and that things they don't want to do at that time can be put off and done later with no problems.
"Tomorrow's just and excuse and you can make it last, forever you"