The administration is wary for a reason. It fears that Schmidt's trip could give a boost to North Korea's young leader, Kim Jong Un, just when Washington is trying to pressure him.
It was only last month when North Korea launched a long-range rocket in violation of U.N. Security Council resolutions. While the U.S. and its allies are seeking harsher penalties against the reclusive communist government. That effort is proving difficult because of a resistance from China, a permanent member of the council. Beijing probably worries that its troublesome ally could respond to any new punishment by conducting a nuclear test.
U.S. officials are also concerned that the high-profile visit could confuse American allies in Asia and suggest a shift in U.S. policy as the administration prepares to install a new secretary of state to succeed Hillary Rodham Clinton. Obama has nominated Massachusetts Sen. John Kerry, the Democratic presidential candidate in 2004.
An imminent change of government in South Korea, a close U.S. friend, is raising questions about whether the two countries can remain in lockstep in their dealings with the North. Newly elected leader Park Geun-hye is expected to seek a more conciliatory approach toward North Korea after she takes up the presidency in February.
This helps to explain why the State Department, which has been a vigorous advocate of social media freedoms around the world, particularly last year during the Arab Spring, made clear it was displeased by the planned "private, humanitarian" visit by Schmidt and former New Mexico Gov. Bill Richardson. Their trip is expected this month.
"We don't think the timing of the visit is helpful and they are well aware of our views," State Department spokeswoman Victoria Nuland said Thursday.
Richardson, a seasoned envoy and a former U.S. ambassador to the United Nations, said Friday that the State Department should not be nervous. In interviews with CBS and CNN, Richardson said they had been planning to visit in December but postponed the trip at the department's request because of the presidential election that month in South Korea.
Richardson said he would raise with North Korea the matter of an American detained last month on suspicion of committing unspecified "hostile" acts against the state; the charge could draw a sentence of 10 years of hard labor. He'll also try to meet with the detainee.
He also said he was concerned about North Korea's nuclear proliferation and this was a "very important juncture" to talk and try to move the North Koreans in the "right direction."
Schmidt, Richardson said, was traveling as a private citizen. But the trip raises questions about whether Google has plans for North Korea.
Schmidt, the company's executive chairman, is a staunch advocate of global Internet access and the power of connectivity in lifting people out of poverty and political oppression. There are few countries where the obstacles are as stark. North Koreans need government permission to interact with foreigners - in person, by phone or by email. Only a tiny portion of the elite class is connected to the Internet.
U.S. law restricts American companies' dealings with North Korea, which is subject to tough penalties because of its nuclear and missile programs. Imports of North Korean goods are prohibited, but travel to North Korea, exports of U.S. goods and investment in the country are allowed, subject to some restrictions, such as on exports of luxury goods.
Richardson has been to North Korea at least a half-dozen times since 1994, including two trips to negotiate the release of detained Americans. His last visit was in 2010.
The detainee, Kenneth Bae, is the fifth American held in North Korea in the past four years. That includes two U.S. journalists who were freed in 2009 after former President Bill Clinton traveled to Pyongyang and met with then-leader Kim Jong Il. Richardson said it was doubtful he and Schmidt would meet with Kim Jong Un, but he expected to talk with officials from the foreign affairs and economic ministries and the military.
North Korea could show good will by freeing Bae. But detainees risk becoming bargaining chips for the North in its tumultuous relationship with Washington. The U.S. retains nearly 30,000 troops in South Korea, a legacy of the 1950-53 Korean War, which ended with a truce, not a peace treaty.
Kim Jong Un's elevation to leadership after his father's death a year ago offered some hope of better relations. But after agreeing last February to an offer of U.S. food aid in exchange for nuclear concessions, North Korea derailed the deal weeks later when it attempted to launch a satellite atop a rocket that the U.S. believes was a test of ballistic missile capabilities.
Relations were set back further by the latest launch, this time successful, which the North again insisted was for a purely peaceful space program.
In the past year, Kim has made at least stylistic changes that hint at more openness, leading some commentators to call for a fresh outreach by U.S. diplomats. That's something that the nominee for secretary of state, Kerry, might support. But there's still little sign of substantive reform.
EDITOR'S NOTE - Matthew Pennington covers U.S.-Asian affairs for The Associated Press.