One of the best non-arguable excuses ever for anything anyone asks you is "work". The various versions are "I am caught/stuck up with work", "work yaar", "I have some work", "have some work at home", "busy with something", "busy with work".
The all time motherhood statement with no explanation of what possible work that could be. If they say it, there is a chance that we may for heavens sake find out a way for their "work" problems. Now that shouldn't happen, can it?
I honestly have come to believe that people saying they are busy with work with no explanations whatever; or without a description of how that work is affecting so many other things too and how they are making other sacrifices; or without a statement that they will make up for the request surely some other time is basically a lie to avoid the request and/or to stop getting a guilty feeling.