While all eyes remain fixated on the nation’s budget woes and the so-called fiscal cliff negotiations, President Barack Obama told NBC News on Sunday that he has more ambitious goals in mind for his second term.

In an exclusive interview with NBC’s “Meet the Press,” Obama said that there are several major issues sitting atop his agenda for the next four years, including immigration, economic growth, energy issues, the environment, and gun violence.

The president discussed efforts to address gun violence and immigration with particular urgency on Sunday.

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"I've said that fixing our broken immigration system is a top priority," he said. "I will introduce legislation in the first year to get that done. I think we have talked about it long enough."

And in the aftermath of December's deadly elementary school shooting in Newtown, Conn., the president vowed to put his "full weight" behind the gun violence recommendations he asked Vice President Joe Biden to generate.

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Obama said that battle would also be fought during the first year of his second term, the success of which the president suggested would hinge upon just how searing the deadly shooting was to the public psyche.

"Will there be resistance? Absolutely there will be resistance," the president told NBC's David Gregory. "And the question then becomes whether we are actually shook up enough by what happened here that it does not just become another one of these routine episodes where it gets a lot of attention for a couple of weeks and then it drifts away. It certainly won't feel like that to me.  This is something that was the worst day of my presidency. And it's not something that I want to see repeated."

Obama also said he was "skeptical" of the National Rifle Association's proposal to put an armed guard in every school, though he said he would not "prejudge" any proposals to address mass shooting events.

Those items alone might constitute an ambitious agenda for a second-term president, who, history suggests, has a limited timetable to accomplish top goals before the waning powers of a lame-duck presidency set in.

But Obama added to that list two other priorities which eluded him in his first term. He said energy and the environment would be a "third thing" on his second term agenda, for instance.

"We've got a huge opportunity around energy. We are producing more energy and America can become an energy exporter," the president said. "How do we do that in a way that also deals with some of the environmental challenges that we have at the same time?"

The president acknowledged, though, that his top priority is preventing automatic tax hikes on all Americans come Jan. 1 as part of the fiscal cliff. That battle has been playing out vividly in Washington during the final days of 2012, and directly involves the fourth priority as described by Obama: stabilizing and growing the economy.

"Part of that is deficit reduction. Part of it is also making sure that we're investing, for example, in rebuilding our infrastructure, which is broken," he said, arguing that the combination of spending cuts elsewhere and new investments would help stabilize the economy.

But Obama's ability to accomplish those four priorities — and then some — could be sapped by the protracted fiscal cliff battle, or any of the other legislative battles he might encounter along the way.

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Immigration reform, for instance, had failed to advance over the objections of Republicans during Obama's first term. He said during the campaign that he would seek comprehensive reforms again in his second term, predicting that, if Republicans fared poorly enough with Hispanic voters during the election, they might relent in their opposition to an immigration bill.

Pete Souza / White House Photo

President Barack Obama is interviewed by David Gregory of NBC's "Meet The Press" in the Blue Room of the White House, Dec. 29, 2012. (Official White House photo by Pete Souza)

In fact, the GOP did not fare particularly well with the increasingly important bloc of Latino voters, but the question of whether they would relent on immigration reform was an untested proposition.

Other tough battles that could inhibit these goals include pending Cabinet confirmations. While Obama has nominated a new secretary of state — Massachusetts Sen. John Kerry — he denied having settled upon former Sen. Chuck Hagel, R-Neb., as his new secretary of defense. But Obama also shielded Hagel, reportedly a front-runner for the defense gig, by saying he sees nothing in the former senator's record as disqualifying.

And there were other second term commitments Obama resisted; he would not commit to significant reforms to entitlement programs like Medicare and Social Security during the first year of his second term, for instance.

At several points in his "Meet the Press" appearance, Obama referenced President Abraham Lincoln and the recently-released film about Lincoln's pursuit of the 13th Amendment, and the trade-offs needed to achieve that goal. Obama invoked that example on both gun control and the fiscal cliff, saying that while he was not comparing himself to Lincoln, that movie offered a lesson in the occasional ugliness of political leadership.

"A, I never compare myself to Lincoln and, B, obviously the magnitude of the issues are quite different from the Civil War and slavery," he said. "The point, though, is democracy's always been messy. And we're a big, diverse country that is constantly sort of arguing about all kinds of stuff.  But eventually we do the right thing."