“The president and his allies need to get serious about spending, and the debt-limit debate is the perfect time for it,” Senate Republican leader Mitch McConnell of Kentucky said in a statement.

A month to the day of the elementary school shooting in Newtown, Conn., Obama said he expected later this week to present his proposals for reducing gun violence. He said he intended to “vigorously pursue” them, but he acknowledged that Congress is unlikely to do all that he asks.

“Will all of them get through this Congress? I don’t know,” the president said, adding, “If there is a step we can take that will save even one child from what happened in Newtown, we should take that step.”

Obama declined to offer specifics on what he’ll propose.

But he said he continued to support more stringent background checks, a “meaningful” assault-weapons ban and the ability to keep high-capacity magazine clips “out of the hands of folks who shouldn’t have them.”

The administration also is expected to pursue some measures it can enact without congressional authorization, including improving how it tracks guns that fall into the hands of criminals.

The president warned against a "rush to judgment," after criticism that thus far he’s picked only white men for top Cabinet positions in his second term. He argued that he had “as diverse if not a more diverse” White House and Cabinet in his first term than other administrations, and that he’d build on that record in his second.

"Until you’ve seen what my overall team looks like, it’s premature to assume that somehow we’re going backwards,” he said. “We’re not going backwards, we’re going forward.”

David Lightman contributed to this report.