“Keeping our country safe: Isn’t that the first job of government?” said Senator Christopher S. Bond, a Republican from Missouri and the vice chairman of the Senate Intelligence Committee. “If we have just a minimalist counterterrorism strategy, the Taliban will come back over the mountains from Pakistan, and they will be followed by their co-conspirators from the Al Qaeda organization.”

Cost is far from the only concern about escalating the war. The debate intensified last week amid disclosures that the United States ambassador to Afghanistan, Karl W. Eikenberry, had sent cables to Washington expressing his reservations about deploying additional troops, citing weak Afghan leadership and widening corruption.

That kind of doubt could also make some in Congress hesitant to support an expansion of the war, especially with the midterm elections coming next year.

Representative David R. Obey, a Democrat from Wisconsin who heads the House Appropriations Committee, said recently that sending more troops to Afghanistan could drain the Treasury and “devour virtually any other priorities that the president or anyone in Congress had.”

Representative John Murtha, Democrat of Pennsylvania and chairman of a subcommittee on defense appropriations, said in an interview that because of concerns about President Hamid Karzai of Afghanistan, he thought a majority of the 258 Democrats in the House would vote against any bill to pay for more troops. “A month ago, I would have said 60 to 70,” he said.

“Can you pass one?” Mr. Murtha said. “It depends on the Republicans.”

Mr. Murtha said he opposed sending more troops, though he would support any decision Mr. Obama made. He said he was concerned that even without a supplemental bill, total spending on the Iraq and Afghanistan wars would surge past $1 trillion next year, which could hamper the economy for years to come.

Others said some Republicans could find it hard to justify a yes vote on troops after criticizing Mr. Obama for his spending. Some liberal Democrats said voters who had been drawn to Mr. Obama for his early opposition to the Iraq war could become disenchanted if he approved a major expansion in Afghanistan.