Joint Chiefs of Staff head Adm Mike Mullen, Defense Secretary Robert Gates and Secretary of State Hillary Clinton all addressed congressional committees on the issue.
"This is a huge commitment. It's the right commitment. And it gives us the forces to turn this thing around," Adm Mullen said.
He said that while there were no guarantees, he expected to "make significant headway in the next 18-24 months".
Mr Gates warned that failure to act "would mean a Taliban takeover of much, if not most, of the country" and the creation of a sanctuary for al-Qaeda militants.
But senior Republican John McCain warned that although the strategy would succeed, US and UK troop casualties would rise in the short term, and he criticised Mr Obama's target date for withdrawal.
"We need to make it clear to the enemy that we're going to succeed and we are going to stay as long as necessary to succeed," he said.
Sceptical
The 30,000 additional service personnel will take the US military presence in Afghanistan to over 100,000.
MARDELL'S AMERICA Mr Obama's top team have been on Capitol Hill trying to convince the serious and senior elected politicians that this is the right strategy Read Mark Mardell's thoughts in full
America has asked for 10,000 more forces from Nato allies to help win a war that has in recent months turned increasingly bloody.
Nato Secretary General Anders Fogh Rasmussen says other Nato countries will provide at least 5,000 extra personnel, and "probably a few thousand on top of that".
But the full extent of additional resources coming from Nato allies remains unclear.
Britain, Georgia, Poland and Slovakia have all pledged more soldiers but other nations such as France, Germany, Italy and Denmark are being more cautious.
It is expected that some countries will declare their intentions over the next two days but just how many is still not clear, reports BBC defence and security correspondent Nick Childs from Brussels.
Many Nato governments face publics even more sceptical about the mission than those of the US and Britain.
It is also emerging that some of those 5,000 extra non-US troops will not be entirely new - they will be forces that were sent out temporarily to support the Afghan elections that will now be staying on.
A senior US official has said this is a process that is going to take days and weeks.
But Nato officials believe that, at the end of it, some 20 countries will end up pledging extra resources, our correspondent says.