Further abroad, the most immediate chance for newly energized Senate Republicans to weigh in on U.S. relations with China will come when Obama travels to Beijing next week to talk with Chinese leaders about a long list of festering disputes with the world's second-largest economy.
Obama's reception is likely to be chilly. On Wednesday, the state-run Global Times delivered a broadside, noting that the GOP Senate victory "further crippled" the lame-duck president.
"Obama always utters 'Yes, we can,' which led to the high expectations people had for him," the editorial said. "But he has done an insipid job, offering nearly nothing to his supporters. US society has grown tired of his banality."
Obama's meeting with Chinese President Xi Jinping will include a discussion of widening U.S. concerns about cyberspying by China's government and military and reports of attacks on U.S. technology companies. China has rejected the claims as unfounded.
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In the past, the White House has also criticized China for its human rights record and issued warnings about increasingly assertive naval actions in disputed waters of the East and South China Seas.
Obama's trip is expected to talks with other with Asian leaders and an informal meeting with Russian President Vladimir Putin. Negotiations with Asian countries on moving stalled trade talks forward have been hampered by congressional foot-dragging on granting the White House a freer hand.
Part of that opposition has come from Democrats whose labor union supporters oppose those trade deals, according to Alastair Newton, a political analyst at Nomura International.
"The optimistic view is that trade is one area where Mr. Obama and the Republicans should be able to find common ground," he said in a note Wednesday.
But even if approved, any new trade deals would be offset by the ongoing slowdown of Asian and European economies.
With a deadline looming this month in the latest round of talks with Iran over its nuclear program, the tone of the new Senate majority's approach to ongoing talks will likely turn more hawkish.
But it remains to be seen how the leadership shift will affect the outcome. Iran's negotiating position has been much more heavily impacted by ongoing economic sanctions that have been made all the more painful by the recent slide in the price of oil, which has funded generous consumer subsidies.
Rising domestic unemployment and inflation, along with falling gross domestic product, will continue to exert more pressure on Tehran than any new policy statements from Republicans. But a hawkish GOP-controlled Senate could also demand stricter terms to any eventual nuclear weapons deal.
Moscow is expecting little change in Washington's policy on trade and economic sanctions imposed following Russia's seizure of Crimea from Ukraine. Beginning in March, the U.S. imposed a series of increasingly tighter restrictions on individuals close to Putin. Those were followed by a wider set of moves, including bank assets freezes, which were joined by the EU, Japan and Australia.
If anything, Moscow expects those sanctions to get tougher. On Wednesday, state-run TASS news agency quoted several Russian analysts as warning that the Senate shift would prolong the standoff.
"The Republicans' victory in the US congressional mid-terms is evidence the Cold War, which the United States is imposing on Russia, is bound to last," Russian Academy of Sciences member Sergey Rogov told TASS. "By getting back to it we have turned 30 years younger in the negative sense."