"Has the US paid its debt of several billions of promised funds to the UN yet?"

We're basically paid up. See link below. The US agreed to pay after the UN agreed to abide by better accounting procedures and external audits and caps the percentage of the UN budget the US would be asked to pay at 25%. The US wasn't the only government to withhold payment due to questionable accounting practices: The Dutch Government will resume payment after Director Arlacchi has shown the will to reform the organisation, and after two upcoming reports have been released. One from an external accountants and one report from a special UN Inspector. The UN has a slightly different view and isn't happy with the changes Congress insists on, of course.

Status of U.S. Payments to the UN

"The only question now is whether the UN will in fact bail W out by his election-inspired 30 June deadline."

Why does that matter? The June 30th deadline is a show of good faith, one for which the UN is irrelevant (as in so many things). What matters to the Iraqis is the election in January. That's when they get to say what government they want. That, dianavan, is the reason so many Iraqis are trying to help resolve the scattered uprisings peacefully. They see that all the uprisings did was to induce the US to bring in more troops and scare the fainted hearted UN away. It helps that the people behind the uprisings are not popular within Iraq. The notion that they could use violence to come to power is an anathma to most Iraqis.