UNITED NATIONS, Sept. 17 — Just five days ago, President Bush's strong appeal to the United Nations for collective action on Iraq allayed world suspicion that the United States was a go-it-alone superpower bent on war and forged a broad consensus that Iraq must give up any weapons of mass destruction or face the consequences.

Now Iraq's sudden offer to readmit international weapons inspectors has turned the world again, and left Mr. Bush scrambling with mixed success to press his case for disarming Iraq and dislodging Saddam Hussein as the next milestone in his campaign against terrorism.

In Washington today, Vice President Dick Cheney lobbied Congress for swift action on a resolution authorizing force against Iraq, and the Senate Democratic leader, Tom Daschle, who had earlier said a debate might take a long time, predicted a vote "well before the election." Asked why, Mr. Daschle said that the administration had done much of what Democrats wanted, by going to the United Nations and consulting Congress, and that "now we are reciprocating."

But here in the Security Council, the hard work of multilateralism was just beginning, and the diplomatic lifting will be heavy. Russia, France and crucial Arab allies all expressed skepticism about the need for a new Security Council resolution in light of Iraq's offer, despite Secretary of State Colin L. Powell's insistence that "We've seen this game before."

"What has changed in the last few days is not the letter that came in yesterday," Secretary Powell said. "It's the full will of the international community being directed to this problem. And it is the international community, through its agency, the United Nations and the Security Council, that should make the judgment as to when, where, if, under what set of circumstances and with what potential consequences" Iraq must comply with a string of past United Nations resolutions.

The Bush administration showed not the slightest indication to heed entreaties from Russia and France — each with veto power over any Council resolution — and Arab countries to take Iraq's offer at face value. Pressing his argument with Americans, Mr. Bush set the tone by warning schoolchildren in Tennessee, "You can't be fooled again."

In short order, the White House released a detailed chronology of Mr. Hussein's past obstruction of United Nations efforts, including his repeated refusal to give teams access to sites they sought to inspect.

Kenneth Pollack, an Iraq expert at the Brookings Institution, said that by allowing the return of inspectors, Mr. Hussein had effectively agreed to Security Council resolution 1284 of December 1999, which sets a much lower threshold for inspections than the Bush administration would like.

"We've really got our work cut out for us," Mr. Pollack said. "I've always opposed going down the inspections route, because at the end of the day, you are betting that Saddam won't give in, and his past record always indicated he would give in. What's so interesting now is that he's given in at the ideal moment: really early, when it messes us up."

One State Department official acknowledged that any significant delay at the United Nations could re-open differences between Secretary Powell and administration hawks led by Mr. Cheney and Defense Secretary Donald H. Rumsfeld, who have been highly skeptical about the utility of weapons inspectors.

"I wouldn't be surprised if there are some who will use this to point out the dangers of engaging multilaterally," the official said.

For now, senior officials said they would keep up pressure in foreign capitals and here in the Security Council to follow up on Mr. Bush's demand for United Nations action, and diplomats braced for a siege.

"If I were on the Security Council, which I'm not, I would in the next days sleep with my eyes open and the boots on," said the Danish foreign minister, Per Stig Moller, whose country currently holds the presidency of the European Union.

The administration was not completely surprised by Iraq's offer, which had been rumored here for much of Monday and drafted in part with the participation of Secretary General Kofi Annan. Washington's initial response was swift, skeptical and in sync, from the State Department to the White House.

But the early timing of Mr. Hussein's move nevertheless seemed to take the administration a bit aback, and some officials feared it could offer Russia, China and France an opportunity to slow the process.

That is particularly troublesome to those administration officials who believe they have to get through the process in a month or two because military action, if required, would almost certainly have to take place in January or February. Only then is it cool enough in the desert for soldiers to wear full chemical and biological protective gear.

"We built in some time for Saddam to play around with the U.N.," one senior official said this week. "But not much time, and we have to convince the rest of the Security Council that the old timelines — 60 days for the inspectors to `assess' what needs to be done — won't work."

Both Republican and Democratic lawmakers, who are to discuss Iraq with Mr. Bush on Wednesday, rallied behind him to bolster his hand in the United Nations. Mr. Daschle said he was "still very skeptical about Saddam Hussein's intent and position."

Asked if he would support a resolution of force that calls for a new Iraqi government, he said Democrats "have been supportive of a regime change from the very beginning."

Representative Richard A. Gephardt, the House Democratic leader, said, "After 12 years of Saddam Hussein's defiance of United Nations resolutions, his regime's new offer to admit inspectors does not address my concerns about the threat he poses to the United States and the international community."