(FORTUNE Magazine) – Usually, by this time in an election cycle, the most important people in the country are not pundits, pollsters, or politicians. The People to See are real estate agents in Washington, D.C. Aides to the incoming President are clamoring for residences in the tony sections of Cleveland Park or Georgetown, while the old guard is selling out to the highest bidder. Not this year. Washington home prices, like the entire voting population, are depressed by the election results.

As FORTUNE went to press, we didn't know who the next President would be. Furthermore, we didn't know when we would know. Will it be after Florida completes counting its overseas ballots on Nov. 17? After the electors meet on Dec. 17? By Inauguration Day on Jan. 20, 2001? The uncertainty was riveting the nation and compelling legal scholars to ponder the potential for a constitutional crisis. Nobody had seen anything like it before. Oh, sure, Kennedy and Nixon were close in 1960--but not like this. And forget comparisons with 1888, when Grover Cleveland won the popular vote but lost to Benjamin Harrison in the Electoral College. That was 112 years ago, for God's sake, when there were no computers to count votes--and a lot fewer lawyers to challenge the results.

Most people assume that the next President--whoever he is--won't be able to accomplish much. He will have won with such a narrow majority, the thinking goes, that he will not be able to rally support for his agenda. The House and Senate will be so narrowly divided by party and so riven by partisanship that nothing of substance will ever be accomplished.

Well, yes and no. On matters of major significance, the new President has probably inherited the mother of all gridlock. This election was about Big Issues. Social Security. Medicare. Education reform. Prescription drugs. We can safely predict that absolutely nothing will happen on any of those.

At the same time, there is a fair amount a President can do all by himself. Most important, he can conduct foreign policy and temporarily commit U.S. troops abroad without congressional approval. He can issue executive orders. Bill Clinton unilaterally protected millions of acres out west from development by declaring them national monuments.

A President also appoints the policymaking tier of his entire government. In Al Gore's Justice Department, the Microsoft antitrust case would likely go on energetically. George W. Bush's regulators could let Microsoft off the hook. One pending proposal abhorred by business leaders that would disappear under Bush but continue under Gore is an effort by the Occupational Safety and Health Administration (OSHA) to require companies to spend heavily to reduce repetitive-motion injuries. The same sort of divergence would likely occur on issues ranging from gun control enforcement to tobacco regulation.

Of course, there's a limit to what any President can do alone. While he can nominate people to crucial jobs, the Senate must approve most of his choices. With the chamber so closely divided, chances are the new President will be unable to win confirmation of anyone whose views are either too liberal or too conservative. Bush, for example, could not appoint any Clarence Thomas types to the Supreme Court. That means that on abortion it is highly unlikely women will lose their right to choose. Conversely, Gore could not name any whale huggers to lead the Environmental Protection Agency, which could slow that agency's effort to press for cleaner air and water, not to mention cleaner cars.

Congress, not the President, usually holds the real power in Washington. But in keeping with this confounding election, the narrow partisan splits in the House and Senate mean that no party will be truly in charge on Capitol Hill. If the new President wants to pass any substantive legislation, he will have to do something rare in Washington: build coalitions among various assortments of Democrats and Republicans. In particular, Bush would have to woo and win over the 30 or so conservative Democrats who constitute the House's Blue Dog caucus. Gore would need to court a small collection of moderate Republicans. Together, these groups hold the balance of power. If Bush reduces his large tax-cut proposal, or if Gore tempers his ambitious spending plans, Congress might be able to compromise on budget matters. Might. "The only legislation that will pass will be center right, not extreme right and certainly not left of center," says Texas Congressman Charles Stenholm, a leading Blue Dog.

Not even the most skillful politicking will enable the new President to fix Medicare and Social Security, the government's most troubled programs. The problem isn't just partisan division; it is the American people's lack of consensus about what they really want. By splitting their votes so evenly between Republicans and Democrats, Americans said, in effect, "We don't know what to do." As a consequence, legislation on derivative issues like adding a prescription-drug benefit to Medicare or writing a bill of rights that lets patients sue their HMOs will also be difficult to pass. The success of any particular initiative will depend on an ever-shifting cast of characters in Congress. "A few dozen lawmakers will control the agenda, but not the same lawmakers," says Bruce Josten of the U.S. Chamber of Commerce. "The challenge will be to find which are the few dozen who control on which issues."

If Bush winds up in the White House, he will face the ultimate test of his campaign promise to bring people together. Gore did not campaign on that promise, but to be effective, he would have to govern on it. The days of cronyism and partisan purity are over. The pressure on the new President to appoint women and minorities to his Cabinet may be greater than ever. But what each man really should do is appoint several Cabinet members from the opposite party--in other words, create a coalition government. If the next President manages to forge a bipartisan consensus in the aftermath of this tumultuous election, he will have accomplished a political miracle. If he fails, watch out. The election of 2004 could be even worse.

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