Seoul (CNN) Less than 50 days into the job, US Secretary of State Rex Tillerson has arrived in South Korea facing a host of issues that would test even the most seasoned diplomat.

The impeachment of President Park Geun-hye one week ago has not only upended domestic politics, it has raised questions over the balance of Washington-Seoul relations at a time of heightened tensions on the Korean peninsula.

Tillerson has questioned US policy on North Korea and is working on a new approach after declaring 20 years of previous policies "have failed."

He visited the demilitarized zone (DMZ), the heavily fortified border between South and North Korea, Friday morning, after which he is due to meet acting President Hwang Kyo-ahn and Foreign Minister Yun Byung-se.

Tillerson is expected to seek assurances that South Korea will continue to honor an agreement to deploy the Terminal High Altitude Area Defense (THAAD) system, the first parts of which arrived in South Korea earlier this month

Next government?

Koreans will go to the polls on May 9 to choose Park's replacement, after which everyone Tillerson meets with may be out of a job. Hwang has already said he won't be contesting his party's leadership.

The upcoming election is expected to result in a swing to the left, likely in favor of the Democratic United Party's Moon Jae-in, who narrowly lost to Park in 2012 and has led opinion polls since her ouster.

Moon's party has been critical of the THAAD agreement and suggested it should be renegotiated, saying Park should have sought the approval of the National Assembly before deployment began.

Their conservative critics, on the other hand, have accused them of seeking to appease North Korea and of being too close to China, which has adamantly opposed the weapons system

Democratic United Party lawmaker Song Young-gil in his office in Seoul, South Korea on March 13, 2017.

In a busy election office in downtown Seoul, alongside rooms crammed with staff and computers, Democratic lawmaker Song Young-gil rejected accusations that his party is "anti-American" and said South Koreans "can decide our destiny."

"The United States and President Trump should respect the new democratic government," said Song, who is running Moon's campaign for the presidency.

He dismissed concerns over a delay in THAAD's deployment, pointing out the system would not protect much of the country, including the nearly 26 million people living in the Seoul metro area.

"It's not urgent," he said. "The more urgent critical thing is how we can prevent (North Korean) nuclear testing, the sixth test."

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'Very dangerous situation'

Conservatives have argued that any shift from the current position on THAAD will be a retreat in the face of pressure from Beijing and Pyongyang.

Kim Young-woo, a conservative lawmaker and chairman of the Korean National Assembly's Defense Commission, told CNN that "the whole Korean peninsula is facing a very dangerous situation now."

He said that if a future government attempted to renegotiate THAAD's deployment "our alliance (with the US) could be weakened."

In the face of Chinese aggression, Kim said the US could consider deploying mobile tactical nuclear weapons to South Korea -- which has been nuclear free since 1991.

Song said Seoul should be able to work with Beijing to "reduce their concerns," adding "we can seek the third solution between beyond the pro or anti (THAAD)."

He added that it is Pyongyang that benefits most from the disagreement. "The chasm between China and (South) Korea and the US, they may enjoy this situation," he said.

Eunjung Lim, a Korea expert at Johns Hopkins University, agreed.

"I don't think THAAD is the reason (for) North Korea's provocations, but they might use this opportunity to estrange South Korea, China, and the US," she said.

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Time to talk?

While Song's party has been keen to reassure Washington that it is open to discussion on THAAD, opposition to the system and the increased militarization of the Korean peninsula was a key part of protests that helped bring down Park.

"The decision made by the government to deploy THAAD was not democratic at all," said Baek Ga-yoon, coordinator for the Center for Peace and Disarmament, which advocates for a nuclear-free Korean peninsula.

She accused acting-President Hwang of taking advantage of the political instability around Park's impeachment to press ahead with THAAD's deployment "without any agreement from the National Assembly and the villagers of Seongju," where locals have long protested the system's installation.

Being opposed to THAAD does not mean people are against or even skeptical of the US-South Korean alliance, Baek said, but she warned that current rhetoric over North Korea risked an "endless arms race."

"It's a vicious circle," she said. "If you deploy THAAD now you're going to later on make an argument to deploy Patriot missiles and then another weapon."

by Echoing arguments analysts -- who point to the failure of sanctions and military build-up to prevent North Korea's nuclear testing -- Baek said she and other civil society activists feel "the only solution is direct negotiation."

"It may sound very naive, but we already witnessed that a hostile strategy against North Korea (pursued by Park's government) and the US government is not effective at all," she said.