Senior administration officials told the Times that the financial implications of more troops has become a volatile issue as the president works to push a costly health care plan through Congress and the government budget deficit is soaring.
The cost estimates of adding 40,000 U.S. forces and increasing Afghan security are $40 to $54 billion a year according to officials, and even if less troops are sent, the White House formula would remain constant at about $1 million per soldier.
Winning support for additional Afghan spending is likely to be a difficult task for Obama and would require support from Republicans to counter Democratic opposition.
Obama, who has spent more than two months mulling Gen. Stanley McChrystal's request for more troops, is under pressure by some Republicans to make a decision as soon as possible.
GOP leaders have criticized his domestic spending and have urged him to provide McChrystal with the resources he needs in Afghanistan.
The president asserted Friday he doesn't want the next move to be seen as an "open-ended commitment."
In a joint news conference with Japanese Prime Minister Yukio Hatoyama, Obama also said he was bent on "getting this right." He denied that his administration has been dithering and said that whatever policy change he announces must be aimed at protecting America from terrorist networks.
Brown said Washington and London "need our other NATO allies to help" and that "we could probably get another 5,000 forces into Afghanistan."
Although his election victory was widely perceived in the West as fraudulent, Karzai's inauguration speech on Thursday is due to be attended by British Foreign Secretary David Miliband and Secretary of State Hillary Clinton.
NATO commanders believe the Taliban will attempt to disrupt the day, with an attack in Kabul or an atrocity elsewhere.
"There is a sense from Karzai, sometimes, that this is someone else's war. He needs to show this is a battle to defend the heart and soul of his own country," a senior NATO source said.
The Times of London and the Associated Press contributed to this report.