A Washington Post-ABC News poll found last week that 46 per cent of Americans support a large influx of troops to battle Taliban fighters and train the Afghan military, while 45 per cent favour a smaller number to focus on training Afghan security forces.
But the US commander-in-chief said he believes the public will support a new strategy once the details are announced.
"After eight years, some of those years in which we did not have, I think, either the resources or the strategy to get the job done, it is my intention to finish the job," Obama said at a news conference with Manmohan Singh, the visiting Indian prime minister, at the White House on Tuesday.
"I will be making an announcement to the American people about how we intend to move forward; I will be doing so shortly."
Al Jazeera's Rosiland Jordan, reporting from Washington, said Obama seemed to indicate some form of additional US troop deployment.
But aside from pressures at home, he will have to also overcome growing political pressure in Canada, France and the UK against additional deployment as the Nato allies count the cost of the increasingly deadly war against the Taliban, our correspondent said.
The US currently has nearly 68,000 troops deployed to fight a resurgent Taliban and al-Qaeda in Afghanistan. As Obama debates a revised strategy in the eight-year war, officials say he is considering four options.
One option is the request put forward by the top US commander in Afghanistan, General Stanley McChrystal, for 40,000 more troops to secure the towns and cities.
Another option, said to be carrying the most favour among officials, is an increase of 30,000. Washington could then try to convince Nato allies to contribute, bringing the number of troops to the 40,000 McChrystal recommended.
Options three and four include significantly lower troop deployments, from 20,000 to 15,000, most of who would serve as trainers for the Afghan security forces.
The US leader will have to appeal not just to the Nato leadership but also the populations in member countries to avoid creating an impression that the US is an occupying or colonising power inside Afghanistan.
Obama's decision has also been complicated by concerns about corruption and governance in the administration of Hamid Karzai, the Afghan president.
Karzai was sworn in for a second term last week after an election marred by widespread fraud and farce as his main challenger refused to take part in a second round run-off.
US officials and Western diplomats say they expect Obama's announcement before a Nato meeting on December 7 in Europe in which alliance members could agree to send thousands of additional trainers to Afghanistan.
Obama and his advisers have debated options ranging from sending the tens of thousands more troops requested by General Stanley McChrystal, the top US and Nato commander in Afghanistan, to limiting troop increases and concentrating on attacking al-Qaeda targets.
Reports have suggested that the advisers are rallying around options that would see a deployment of between 30,000 and 40,000 troops and trainers sent to Afghanistan.