President Obama is bracing for more acrimony with Congress over spending priorities even as his aides paint a hopeful picture of unity with House Republicans.

Speaking to school children at the White House Monday, the president told them that on priorities like ensuring they can go to college without a huge debt burden and making sure public schools are strong, he expects push-back from Capitol Hill.

"[W]e've got to make sure that we continue to make those investments," he said, "and that's going to be a big battle. We're gonna have some people who disagree with that because their basic attitude is that government generally is not something that is particularly important and that a lot of this stuff should be happening at the local level."

But Mr. Obama's staff, fresh off a hard-fought budget deal Friday night with House Republicans which averted a government shutdown, point to an increasingly cooperative, if divided, government.

"The agreement that we reached on Friday, that the president reached on Friday laid a predicate," White House Press Secretary Jay Carney told reporters.

"All of this stuff is hard. All of these negotiations will be difficult. But what I think the American people should take away from what they've seen happen in recent days is that there is reason to hope that we can work together and get the work done that the American people expect us to get done."

House Speaker John Boehner, R-Ohio, doesn't disagree with that notion, saying that he and President Obama have gained a better understanding of one another in recent weeks. "I feel we've built a fairly decent foundation leading into the next fight," he told Fox News Channel's Bill Hemmer in an exclusive interview Monday.

Still, Friday's eleventh hour agreement between Hill Republicans and Democrats and the White House, was only the first hurdle, says the speaker, "[W]e got through this one successfully. The next one is going to be much more difficult. And he knows it and I know it." Mr. Boehner was referring to the issue of the raising of the nation's debt ceiling, over which political lines have already been drawn.

If the president's comments Monday reveal anything about the forthcoming talks, it's how ugly such discussions can be. "[S]ometimes I get a little," Mr. Obama paused, "frustrated that the debates aren't more honest or as clear as I'd like them to be."

Mr. Obama's advisors say Boehner was an honest broker in the budget talks, but hinted his caucus was a much tougher sell.

"I get along with him very well," Boehner said of his relationship with the president. "That doesn't mean that we don't have very different visions for what the role of the federal government should be in our society."

But the speaker added that he sees the potential for more cooperation, "I can tell you that privately, I have encouraged the president, 'Mr. President, lock arms with me, let's jump out of the boat together.'"