NEW YORK – Few Americans cast their ballot in the recent mid-term elections on the basis of foreign policy. While it may be difficult for people around the world to comprehend this, given the global reach of the United States, it is an undeniable fact.

Most Americans are, after all, preoccupied with the US economy’s sluggish growth and persistent high unemployment. The world’s challenges seem far removed from their day-to-day lives. The Cold War ended a generation ago; the terror attacks of September 11, 2001, are nearly a decade in the past. Most Americans do not feel the sacrifices associated with the large troop presence and ongoing conflicts in Afghanistan and Iraq.

But the fact that foreign policy did not materially affect the November elections does not mean that the results will not affect US foreign policy. They will, but in ways that are inconsistent and even surprising.

One relationship sure to be influenced by Republican gains will be that between the US and Russia. Quick or easy Senate approval of the New START arms-control treaty is highly unlikely, given stated concerns about verification and the protection of US missile-defense programs; instead, we can expect delays and, possibly, attempts to amend what the two governments already agreed upon.

Congress may also prove less willing to remove hurdles to Russia’s admission to the World Trade Organization, given what is widely judged to be its leaders’ anti-democratic behavior.

China, too, will feel the results of the new balance in Congress. Pressure was already growing to introduce trade sanctions in response to China’s refusal to allow its currency to rise to a natural level against the dollar. Such pressure will likely grow, given concerns over Chinese behavior both at home and abroad.

Moreover, Congress will resist rolling back any of the long-standing economic sanctions against Cuba. President Barack Obama has the authority to take some small steps on his own to normalize ties, but substantial change to US policy requires Congress to act – and Congress wants to see fundamental change in Cuba before it does so.

There will be other consequences stemming from the election. What little chance there was of the US backing any global plan to limit or tax carbon emissions has disappeared. Improvement in US performance on climate change will have to come from innovation and increased energy efficiency.

One can anticipate the Republicans, now in control of the House of Representatives, exploiting their ability to convene hearings to question and review foreign policy.

Depending on how this power is used (or abused), it can be beneficial (exercising needed oversight and increasing the transparency of policy and policy-making) or destructive (if, for example, hearings degenerate into politically motivated attacks on administration officials and policies).

In many other areas, continuity can be expected to trump change. This comes as little surprise, as America’s Constitution and political system delegate most of the initiative on foreign policy and defense to the president.

Yes, Congress must declare war, approve spending, agree to most senior appointments, and (in the case of the Senate) ratify treaties, but the president has enormous latitude when it comes to carrying out diplomacy and using military force in situations other than war, which tend to be most situations.

One area of probable continuity is the Middle East, where Obama will continue to try to broker a deal between Israelis and Palestinians and press Iran not to develop nuclear weapons. (Republicans, however will argue for putting less pressure on Israel to compromise and more pressure on Iran.)  But he can expect considerable backing from Republicans if he wants to maintain a sizeable US military presence in Afghanistan beyond this July, or a modest military presence in Iraq beyond the end of 2011.

Questions abound when it comes to foreign economic policy, however. Three completed trade agreements (with South Korea, Panama, and Colombia) have been languishing for years, mostly because of deep opposition to free trade from labor unions and the Democratic Party. Republicans have historically been more supportive of such bilateral free-trade agreements.

But will the new generation of Republicans continue this tradition? There is a fair chance that one or more of these bilateral accords will be approved (in part because the Obama administration seems finally to have recognized that trade can generate good jobs), but it is far less certain that the president will gain the authority needed to negotiate a new global trade deal.

An even bigger question mark hovers over what might be the greatest national security concern of all: the federal budget deficit. Failure to address the deficit (and the mounting debt) will create pressures to reduce what the US spends on foreign aid, intelligence, and defense – although Republicans are more likely than Democrats to protect such spending (except for foreign aid).

Mounting debt also leaves the US vulnerable to the decisions of those who lend it money – or to the vagaries of the market. A dollar crisis could weaken the foundations of American power.

But averting such a crisis requires that the White House and Congress, Democrats and Republicans, agree on a plan for moving the US budget toward balance. Alas, the election makes such agreement more distant than ever.

Richard N. Haass is President of the Council on Foreign Relations.