When President-elect Donald Trump met with Barack Obama in his first conversation since the US election, the outgoing president warned him that one of the biggest crises he faces is on the Korean peninsula, where Kim Jong-un’s penchant for nuclear adventurism could flare up during the US Presidential transition.

It’s difficult to say, however, which Korea, North or South, deserves the most urgent attention. Both are troubling and possibly insoluble. Let’s begin with South Korea.

Park Fights for Political Life

Yes, Trump called President Park Geun-hye the day after his election and assured her of continued US support. The words were no doubt comforting considering that during his campaign he said the US should withdraw its 28,500 troops if South Korea doesn’t pay all the costs for having them there. He also said, not to her but in one of his campaign harangues, that South Korea and Japan should probably have their own nuclear weapons for defense against nuclear-armed North Korea.

Now the question is how the US will maintain the alliance with South Korea while Park fights for her political life. The prevailing view here is that Park herself masterminded the scheme for getting Korea's biggest companies to donate tens of millions of dollars into two foundations from which a long-time sisterly friend siphoned funds while drafting her speeches and poring over confidential state documents. Park was "complicit," say prosecutors, in the scandal in which the woman, said to have won her confidence in shamanistic rituals, has been indicted along with two of her former top aides.

If Park survives, could Trump meet her for a summit? How could she receive him at the Blue House with hundreds of thousands massed on the broad avenue from Seoul City Hall? Struggling to keep her job, might she see him at the United Nations or some international conference? She sent her prime minister to the recent APEC conflab in Peru – a sure sign of her isolation from the rest of the world as well as her own people, who give her an astonishing and depressing 5 percent approval rating.

Her Own Party is Furious

The position of some members of Park’s own party adds to the unease. Park, closeted in the Blue House, faces the wrath of a runaway wing of her "ruling" conservative Saenuri Party plus the unanimous rage of the main opposition Minjoo or Democratic Party and two smaller left-wing parties. The Minjoo, the People’s Party and the Justice Party are united in their resolve to force her out of office but are sure to have trouble agreeing on a candidate to run in the election that must be held in 60 days after the resignation of a president.

Within the American embassy, blockaded by hundreds of policemen as demonstrators swarm by on their way to rows of police buses defending the Gyeongbuk Palace of dynastic kings, diplomatic analysts are working overtime outlining scenarios to fit any contingency ranging from Park’s resignation to a protracted impeachment process to a state of crisis right up to the next scheduled election in December 2017. While police buses block the demonstrators from reaching the Blue House looming beyond the palace grounds, protesters claim to have "encircled it" by challenging police on approaches from the other side.

She Loses the Papers

The crisis is complicated and compounded by the anti-Park policies of conservative newspapers that once defended her. Not just the left-leaning Hankyoreh but also those much larger conservative stalwarts, Chosun Ilbo, JoongAng Ilbo and DongA Ilbo, “ChoJoongDong,” are all critical of her as they catch the populist mood. The National Assembly might spend months in rancorous debate over impeaching her – a step requiring approval of two thirds of its 300 members. The constitutional court then has six months to deliberate before approving impeachment, requiring the ayes of at least six of its nine members.

What is Trump to make of South Korea in this heated atmosphere? It would be difficult for any president to know what to do, but for a newly elected leader with no background on Korea, dealing with South Korea on issues of defense and trade will be perilous indeed.

In this sensitized atmosphere, Trump may have to forget about scaling down the number of troops or doing much about revising the KORUS Free Trade Agreement, which he also criticized during his campaign. (Korea was not among the 12 nations that agreed on the Trans-Pacific Partnership, which President Obama had hoped would be a legacy of his presidency and Trump has promised to ditch.)

Meanwhile, in Pyongyang

North Korea, however, may not give him the luxury of time. In fact, the real danger is the North-South confrontation will worsen while the North conducts more underground nuclear tests and test-fires more missiles.

What if the North finally develops a warhead that fits on the tip of a long-range missile capable of hitting targets anywhere in South Korea or Japan and possibly Hawaii, Alaska or even the US west coast? Trump may be reluctant to stage a “first strike” on North Korea, wiping out missile and nuclear facilities before the North has a chance to use them in action, but there’s no telling when tensions will escalate to the brink of war.

Trump has said that he would like to meet Kim Jong-un, even dine with him on hamburgers. It's not out of the question that he'll suggest a summit, but where? Considering that Kim since taking over after the death of his father Kim Jong-il nearly five years ago has never left North Korea, no one can expect a meeting during a session of the UN General Assembly. Nor is it likely that Trump would meet Kim at the truce village of Panmunjom where Kim has never ventured on any of his visits to military units.

For both Koreas, a critical question is whether the US will be able to install THAAD, the Terminal High Altitude Area Defense batteries needed to blow high-flying North Korean missiles out of the sky. South Korea under Park has approved THAAD, but will a new Korean president, a liberal, support the deal or might THAAD be forgotten in a storm of leftist protest? The betting is that Park will try to ride out the storm through the rest of her term, but what is likely to happen to the U.S.-Korean defense arrangement as she clings to her job?

Those are questions that Trump and his advisers, whoever they are, need to consider carefully while a coalition of conservative, moderate and liberal forces cries for her to step down. For Trump, the challenge will be to navigate among these groupings, while the North exploits political disarray and tries to drive a wedge between the US and South Korea.

Donald Kirk is a longtime Asian analyst and regular contributor to Asia Sentinel