Countries for and against a second resolution are trying to get those who haven't decided how they will vote, on their side.
The French Foreign Minister Dominique de Villepin is visiting Angola, Cameroon and Guinea to persuade them to vote against the resolution.
And the US are trying to get Mexico and Chile to vote with them.
The US Secretary of State Colin Powell reckons nine or 10 of the 15 Council members would support a second resolution.
But he said a US-led attack on Iraq could even happen before Monday's deadline, if the UN votes against the resolution.
Meanwhile, UK Prime Minister Tony Blair is meeting his advisers after an important government minister Clare Short told him she'd quit if there's an attack on Iraq without the UN's permission.