As the U.S.-led coalition hunts down insurgents and other nations appear hesitant to commit troops for an unstable Iraq, President Bush has shifted tactics and now appears ready to move up the date for putting Iraqis in control of their own affairs.

"Ambassador [L. Paul] Bremer sat right here yesterday and talked to me about the Iraqis' desire to be more involved in the governance of their country. And that's a positive development," Bush said Thursday from the Oval Office, where he held an early-morning event to complain about delays in the confirmations of his judicial nominees.

"They are clamoring for it. They are, we believe, ready for it. And they have very strong ideas about how that might be done," National Security Adviser Condoleezza Rice told reporters in an afternoon briefing.

Bremer is now headed back to Baghdad with the administration's ideas about several Iraqi proposals that officials say could lead to an interim government in short order.

Administration officials say it's conceivable that a transfer of power in Iraq could take place even before next year's U.S. presidential election, though officials insist the election is not a factor in the timing.

The administration had strong ideas about the process that should be taken toward Iraqi self-governance, and argued at the United Nations in September that before power could be turned over to the Iraqis, a new constitution had to be written and ratified in a referendum and a new government had to be elected.

But after two days of talks with Bremer, the president no longer seems to mind short-circuiting the democratic process that officials say would take too long.

"There has been concern expressed that the time required to write a constitution — if you are going to go through an election process to determine who should be on the constitutional-writing commission — could eat up a great deal of time, more time than we think would be allowed before we start transferring sovereignty back," said Secretary of State Colin Powell during a press conference with British Foreign Secretary Jack Straw (search).

"It is still important that the Iraqi people have a permanent constitution and elections for a permanent government. Nothing has changed," Rice said. "But what is also important is that we find ways to accelerate the transfer of power to the Iraqis."

Bremer's trip to the United States took on added urgency after Wednesday's truck bomb attack in Nasiriyah killed 31 people. His visit also coincided with a CIA report that said Iraqis are starting to support the insurgency because they're losing faith in the U.S.-led occupation.

U.S. troops in the "Sunni Triangle" (search) area north and east of Baghdad went on the offensive for a second straight night Thursday, hunting enemy insurgents south of Baghdad as part of the U.S. military's new "get-tough" campaign called "Operation Iron Hammer."

"We were able to take one group of individuals, about 10. We killed two, wounded a couple and captured five, of one cell that was shooting mortars," said Brig. Gen. Mark Hertling. 

In addition, Deputy Interior Minister Brig. Gen. Ahmed Ibrahim said police arrested six people, including four foreigners, in operations Thursday. He refused to identify the nationalities, but a policeman, speaking on condition of anonymity, said they included a Syrian, a Yemeni and an Afghan.

At U.S. Central Command headquarters in Tampa, Fla., on Thursday, Gen. John Abizaid (search) said the enemy in Iraq is made up mostly of former regime members, but foreign fighters, extremists and hired criminals are also in the mix. In all, fewer than 5,000 total enemy fighters are operating throughout Iraq.

But, Abizaid said the fighters are well-organized, well-financed, well-armed and highly motivated.

"Violence has increased in the past several weeks and it has increased substantially. Part of the reason is that the enemy has learned to adjust to our tactics, techniques and procedures," he said.

Abizaid said the goal of the enemy is to break the will of the United States and its coalition, to make troops leave. Abizaid said that won't happen despite the fact that Japan has said it will delay sending any troops to Iraq, possibly until next year, and South Korea announced it is capping its contribution to 3,000 soldiers.

Since coalition troops and international organizations have become targets of Iraqi insurgents, Denmark has also rejected a push by two Danish soldiers' unions to bolster its 410-member force by 100 more troops, and Spain and the Netherlands, along with the United Nations and the international Red Cross have been reconsidering their presence.

"There's absolutely no doubt in my mind that with patience, perseverance and courage we will see this thing through," Abizaid said. 

The Iraqi Governing Council argues that transferring more power sooner than later will make life safer for the coalition. Officials say the Council's progress — in economic matters more than security matters — lends confidence to the notion that the Iraqi people may be near ready to manage their own affairs.

"We believe Iraqis are more capable of managing security than Americans ... the dialogue is still continuing with the two partners," said IGC spokesman Hamid al-Kifaey.

The White House agreed.

"The kind of security circumstances and challenges that are being faced on a daily basis are going to be better dealt with by Iraqi security forces, with us in support of them, than by our coalition forces alone," Rice said.

According to the last U.N. resolution, the IGC was to present a timetable for a new constitution in one month from Saturday despite misgivings by the Council, which had indicated a short-term provisional government should precede a constitution.

Now exploring the options, the Bush administration is proposing elections in Iraq in the first half of next year, and says that can occur before a constitution is written. In the meantime, Bremer will consult with the IGC about appointing a special panel to oversee an accelerated transition to Iraqi rule and how to select the provisional government.

That option calls could creating a smaller body within the 24-member council — perhaps 10 people with expanded roles.

Iraq does not have any national voter rolls from the Saddam Hussein days when voters hardly mattered, so one possibility is to follow the Afghan model in which village elders participated in a "Loya Jirga" and Hamid Karzai (search) was chosen as the country's interim leader.

That would not be a perfect one-man, one-vote situation, said a diplomatic source, but it would be a start.

"Circumstances no longer allow us to be that purist. We need to tack and weave," a diplomat familiar with the consultations told Fox News.

Fox News' Jim Angle, Wendell Goler, Bret Baier and The Associated Press contributed to this report.