Yes broken links can hurt you, if the links stay broken for a while. I can't see you getting hurt for having a broken link for only a few days. I think even SE's know that not everyone can fix it right away. The SE just keeps checking that link and if it isn't fixed over a period of time then yes it can have an effect on your
PR.
When a SE finds a broken link it gets directed to a 404 error page. The SE will then leave your site because it reached a 404 error page.
**SE= Search Engine