The Pakistani government appears stable for now, but the United States is worried about what will happen if it falters.

In an interview with FOX News, Secretary of State Hillary Clinton, who traveled to Beirut, Lebanon, Sunday ahead of elections there, said Pakistan's possession of nuclear weapons makes it extra important for the government to keep a lid on the Taliban there. 

"If the worst, the unthinkable, were to happen ,and this advancing Taliban encouraged and supported by Al Qaeda and other extremists were to essentially topple the government for failure to beat them back, then they would have the keys to the nuclear arsenal of Pakistan," Clinton said Saturday.

That is something Clinton said she doesn't even want to contemplate, but explains why the United States is pushing the Pakistani people to come together around a U.S. strategy for keeping their country on a stable track. 

Asenior U.S. official traveling with the secretary said whatever concerns Washington has about the security of Pakistan's nuclear arsenal are longstanding and unrelated to the Taliban's recent advances.

The official indicated that if the Taliban were to succeed in toppling the government of Pakistani President Ali Arif Zardari, the United States believes the likeliest event would be a coup by the military similar to the one that placed Pervez Musharraf in power in 1999. 

On Sunday, Pakistan launched operations against militants in an area currently under a peace agreement but next to the volatile Swat Valley that the government agreed to allow the Taliban to rule.

Recent forays by the Taliban into nearby districts outside of Swat have raised alarms in Pakistan and the West. Interior Ministry chief Rehman Malik said the government is serious about "flushing out" the militants.

A military commander familiar with the operations said "scores" of militants have been killed in the fighting, including a key commander.

A spokesman for Pakistan's president said the government is determined to root out the militants "hell-bent" on destroying the law and order that has been established.

Clinton said the U.S. has worked very hard with the Pakistanis to gain solid assurances that the Pakistani government and military are stable.

As the Pakistani army gets a hold on the area, the official traveling with Clinton said that discussions scheduled in Washington, D.C., in the first week of May between President Obama and Pakistani President Ali Arif Zardari will go on as planned, but Zardari will take a smaller entourage with him so as not to create "temptations" for the Taliban to use the summit period as a window in which to launch attacks.

Clinton said the Obama administration is looking in Pakistan to use the same methods as the Bush administration did in Iraq -- separating out and reconciling with those who are part of an armed campaign for political, cultural and historical reasons from those who are "hard core extremists and terrorists."

"I think that the general principle that we don't associate with these people is absolutely the same. But the opportunity as we found under the Bush Administration in Iraq is worth exploring with those elements of the Taliban that are there because they pay better than the Afghan police force pays, for example," she said. 

"So what we're attempting to do is to follow what turned out to be a smart strategy in Iraq in other places, with the same level of caution, with the same level of skepticism. But understanding that we don't do business with the terrorists. But we may do business with the people who got swept up in some kind of move doesn't necessarily define their attitude toward the United States or the use of violence," Clinton said.

FOX News' James Rosen and Shannon Bream contributed to this report.