Is North Korea on the brink of war?

Politicians and pundits painted a pretty bleak picture of the situation in North Korea on the Sunday talk-show circuit, with South Carolina Sen. Lindsey Graham predicting a "major war" breaking out if Kim Jong Un attacks South Korea.

"The North Koreans need to understand if they attack an American interest or an ally of this country, they're going to pay a heavy price," Graham said on NBC's "Meet The Press" on Sunday. "I could see a major war happening if the North Koreans overplay their hand this time, because the public in South Korea, the United States, and I think the whole region, is fed up with this guy."

"I think we have to convince this new, young, inexperienced leader that he's playing a losing hand," former U.S. Defense Under Secretary Michèle Flournoy said. "The only way out of the box to get the economic development he wants, to get the progress that he wants, is to ratchet back the rhetoric. Come back into compliance with the international obligations."

Since assuming power in late 2011, the provocative Kim has defied U.N. sanctions by continuing to develop North Korea's missile program.

"He's kind of reckless right now," Gen. James Thurman, the top U.S. military commander in South Korea, said on “This Week with George Stephanopoulos" on ABC. "If they decided to, you know, resume hostilities, I think we've got to be ready to go."

Earlier Sunday, U.S. officials said Thurman, who was expected to travel to Washington this week to appear before the Senate and House Armed Services Committees, will instead stay in Seoul as "a prudent measure."

When asked to speculate on the outcome of a war, Graham, a member of the Senate Armed Services Committee, said: "The North loses and the South wins, with our help. That's what happens."

[Related: Rodman says Kim Jong Un wants Obama to ‘call him’]

On "Meet The Press," former New Mexico Gov. Bill Richardson called Kim's leadership "belligerent," but cautioned against U.S. military action.

"I think the goal should not just be to calm them down, to cool the rhetoric down," Richardson said. "The goal has to be [to] get North Korea back to the negotiating table on nuclear proliferation, on de-nuclearization. They have to do it, because that whole Asian area is a tinderbox."

Fox News host Greta Van Susteren, who has visited North Korea three times, said negotiation is not something on the minds of most North Koreans.

"The whole time we were there, all we saw was preparation for war," Van Susteren said. "If you go inside, they have been at war with us since the early 1950s. They think that every single one of us is spending every Saturday night sitting around planning how to get them while we're busy ordering pizzas and Chinese food carryout, they think that we're getting ready for war."

Graham said the United States needs to keep its eye on Syria, too.

"Crazy people and nuclear weapons who proliferate those weapons throughout the world, who support terrorist organizations, are incredibly dangerous," Graham said. "That's why we need to stop Syria from getting chemical. Chemical weapons need to be controlled in Syria; the ayatollahs in Iran are just as crazy as this guy in North Korea."

He added: "This could be a nightmare in the making with these chemical weapons falling into radical Islamists. The number of radical jihadists on the ground in Syria today is growing every day this war goes on."