The legislation includes funds for two Clinton pet projects Â— hiring more teachers and police.
White House Press Secretary Joe Lockhart said the president is likely most proud of the budget's commitment to education and teachers, even though the states have the liberty to use the new funds as they please.
"One of the things we've learned is how important it is to get class sizes down," Lockhart told CBS Early Show Anchor Bryant Gumbel.
Acknowledging the budget package fell short on many of his goals, he nonetheless said the bill represented "real progress" for American families.
While Mr. Clinton thanked party leaders and committee leaders on both sides of the aisle for their tireless effort during the arduous negotiations, he said there is still more to do.
"I ask that we be mindful of all that we still have to accomplish," the president said, referring to gun safety legislation, the patients bill of rights, and raising the minimum wage, among other issues.
The White House had to accept Republican wording to pay the U.S. debt to the United Nations while restricting funding for international family planning programs.
Although Lockhart said the wording was "unwise" on the part of the extreme Republican right wing, he said it is still a good deal.
"We'll be able to pay our dues and not lose our vote at the United Nations," Lockhart explained.
The budget agreement also gave the president victories with buying land for parks and expanding efforts to forgive debts of poor nations.