Open Question: can I claim federal tax withholding exempt?

I am relocating with my employer and they offer a relocaiton bonus of a substantial amount. I would like the entire bonus to help pay off a few bills (medical, etc). I see the button to click for withholding exempt on my on line personnel system, but can I do that? I've also heard of increasing deductions, but by how many?? I need to do this for 2 pay periods (I a paid bi-weekly). Thank you for the information!