The fish should be fine. If you have corals and other inverts then the skimmer is more critical. Either way you should be fine for a while without a skimmer. Some folks run reef tanks without a skimmer at all (I don't, nor do I recommend it). If you're going to go skimmer-less then you'll just need to keep on a strict water change schedule.
Depending on the brand pump you may be able to get a replacement impeller (which is likely the issue).