(By Yuri Gripas/Reuters)

Clinton told members of the Senate Foreign Relations Committee that the Obama administration was going to continue to try to work with Pakistani officials across the political spectrum to achieve its goals in the region.

“We’re going to demand more from them,” she said when pressed on the administration’s strategy. “But we are not going to expect any miracles overnight.”

Clinton’s comments came at a hearing to discuss President Obama’s announcement of a troop drawdown in Afghanistan. But at that hearing – and a concurrent hearing by the House Armed Services Committee -- it was the vexing challenges posed by Pakistan that loomed large at times.

Senate Foreign Relations Committee Chairman John F. Kerry (D-Mass.), who has urged a greater focus on eastern Afghanistan and on Pakistan, noted that while there are estimated to be 50 or 60 al-Qaeda fighters in Afghanistan, there are believed to be countless more on the other side of the border. The United States spends about $120 billion a year in Afghanistan, he added, but spent only $2.8 billion in Pakistan last year.

“I don’t mean to insult Afghanistan or saying anything pejorative about the efforts and what is at stake there -- but in many ways, the Afghanistan war is a sideshow to the main event, if you will, that is next door,” Kerry said.

Clinton noted that the U.S.-Pakistani relationship has long had its ups and downs, and that the Pakistanis have suffered “extraordinary losses” in the fight against the Taliban and other extremists groups.

Relations between the two countries have deteriorated severely since the killing of Osama bin Laden, which exacerbated suspicions that some elements in the Pakistani security forces knew of his whereabouts.

Pakistani public opinion, meantime, has turned decidedly against the United States. A survey released this week by the Pew Research Center found that only 12 percent of Pakistanis said they had a favorable view of the United States. A significant majority of Pakistanis -- 63 percent -- disapproved of the raid that killed the al-Qaeda leader.

“You know, they would be perfectly happy if we picked up and left tomorrow,” Clinton said of the Pakistanis. “But what would we get for it and what would they do with it?”