The United States was looking for the approval of the Security Council, a 15 member body within the United Nations, and especially the support of the five permanent members who have veto power.
Russia did not warm to the idea of the war, plus they have often voted against American proposals in the past. The Chinese did not want an unstable Middle East because they depend on the oil reserves there, but were willing to abstain from voting. France felt like the US had not proven its case that there were WMD's present and that Iraq was actually a threat.
Faced with the prospect of losing a UN vote, we withdrew the resolution and acted unilaterally, that is, by ourselves with a few allies we called The Coalition of the Willing.