I suppose it depends on how one defines "you can handle".
First of all I think the saying is perhaps a distortion of 1Co 10:13 - "No temptation has overtaken you except such as is common to man; but God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will also make the way of escape, that you may be able to bear it" which talks more of God providing a way of avoiding temptation than escaping other difficult situations. That said, it could be argued that particularly brutal trials in life could represent a temptation to abandon our faith in the God who apparently isn't protecting us from them.
During my school days the standard prayer in our daily assemblies included the line "we do not ask for tasks equal to our powers, we ask for powers equal to our tasks". I forget who was quoted as saying "if God brings you to it he will bring you through it", and I suspect that if we are willing to follow God come what may then he will guide us through everything, even if our life changes beyond recognition in the process. If we regard major life changes as meaning we can't handle something then it's entirely possible God will give us things we can't handle. If we expect to do everything in our own strength it's also entirely possible God will give us something we can't handle. If we are willing to hold everything loosely, knowing that ultimately it all belongs to God anyway, and accept that God is in control of our destiny, perhaps it becomes easier to handle things we would rather not face.
If we, like Christ, are truly willing to say "not my will but yours be done", perhaps things become easier. And as with so much else of this nature, it's so easy to write it on a message board and not always so easy to actually live it.