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With voters focused on the country's troubled economy, international crises and the nine-year-old war in Afghanistan were largely ignored in the election campaign.
But armed with a majority in the House of Representatives, Republicans are expected to use their new platform to portray Obama as weak on national security, soft on China and ambivalent about Israel, experts said.
"Congress sets the temperature for a lot of these issues," said Steven Clemons, a senior fellow at the New America Foundation. The atmosphere is "going to become very pugnacious."
"They will complain about whatever he does, and poke holes in whatever he's doing," he said.
As president, Obama still retains a great deal of power in the realm of foreign policy, and the Republicans will be unable to impose a blockade on his international agenda.
"In our system, foreign policy is primarily the province of the executive branch. That's not going to change," a senior US official said.
The Republicans, however, can create headaches by issuing critical resolutions, holding up White House nominations for diplomatic and military posts and launching contentious hearings or investigations.
"It's going to be very messy," Clemons said.
Amid public anxiety over China's economic clout and a resurgence of economic nationalism on both the right and left, lawmakers will probably bring "more pressure to push the Chinese harder on trade and the currency issue," said Stephen Flanagan of the Center for Strategic and International Studies.
On Middle East diplomacy, some analysts said Obama may find it even more difficult to persuade Israel to suspend settlements in the West Bank given the Republicans' triumph at the polls.
Israel enjoys strong support in Congress and Republican lawmakers already have accused Obama of undermining a vital ally by demanding the freeze.
Republicans in Congress also are expected to renew their criticism of the White House over Iran, voicing impatience with efforts to halt Tehran's nuclear program.
"The administration will feel some more heat about further ratcheting up pressure, the idea that time is running out," Flanagan said.
The Republican electoral wave could doom a landmark US-Russia nuclear arms treaty, unless the current Senate manages to pass the accord in its final session, analysts said.
Republicans, who have so far blocked ratification of the new Strategic Arms Reduction Treaty, have argued the accord offers too many concessions and undermines missile defense plans.
Playing to voter concerns about a ballooning budget deficit, the Republicans are likely to take a much more skeptical attitude to international aid, questioning funds for development projects abroad, experts said.
On Afghanistan, Obama will almost certainly come under fire from Republicans over his attempts to promote a peace deal that would include a role for the Taliban at the negotiating table.
"That whole process is going to bring out enormous criticism," Clemons said.
But the Republicans have been supportive of the war in Afghanistan overall, much more than Obama's fellow Democrats.
Republican backing for the war effort is likely to continue, despite grumbling about the planned start of a troop withdrawal in July 2011, said Thomas Donnelly of the American Enterprise Institute.
Administration officials have already made clear the drawdown will likely begin on a small-scale, with perhaps no more than 2,000 troops initially pulling out -- leaving intact a massive presence of about 100,000 American forces.
Despite plans to put Obama's foreign policy under more scrutiny, the newly elected lawmakers face internal divisions with the emergence of the ultra-conservative Tea Party.
The movement's views on foreign policy issues remain a major question mark, as some of its members are at odds with the Republican party's traditional embrace of US global power.
Many Tea Party supporters display an isolationist bent with a deep hostility to any international agreements or treaties, along with a strong skepticism of development aid and diplomacy generally, analysts said.
"Nobody knows exactly what the nature of the Tea Party movement is," Donnelly said.