There's not always time to finish it properly, but there's often a good stopping point halfway. When there's a lot that needs refactoring, I start with one specific thing, and leave the rest for now, so the piece I've bitten off is still small enough that it can be wrapped up in a reasonable amount of time. And the rest will have to wait.
In my current project, there are piece of code that I've wanted to remove for months now. I was working on refactoring it out completely, but there's one place that still uses it, and that wasn't so easy to fix as all the other places where it had become unnecessary. It still needs to be done, but there hasn't been any time. Or urgency, really. But it's still there, taking up space in my head.
They also want to get rid of the old code, but they're not removing it. One of them also has a tendency to interesting structural solutions, though he tends to do it more by adding them than by rewriting what was already there, which has the advantage that it doesn't disrupt the old code that others are working on, and the corresponding disadvantage that the old code survives.
In my current project, there are piece of code that I've wanted to remove for months now. I was working on refactoring it out completely, but there's one place that still uses it, and that wasn't so easy to fix as all the other places where it had become unnecessary. It still needs to be done, but there hasn't been any time. Or urgency, really. But it's still there, taking up space in my head.