To my ears, it sounds awkward. I would at the very least change 'things' to 'requests', as that is what the first sentences seem to apply you are going for.
'Important' might be alright depending on the context, but 'necessary' can be an appropriate (or perhaps even more appropriate) fit here as well.
Where the second sentence part goes (after the comma), 'because we can't do everything' sounds more natural to me.
Mind you, I'm not a native English speaker, but I have spend a fair amount of time with both English and American people.