BONN, DEC. 3 -- Since the Berlin Wall burst open 13 months ago, all Helmut Kohl has had to do is negotiate the merger of the two Germanys, persuade the rest of the world to support unification and get himself reelected.

Now comes the hard part.

The first chancellor of the reunited Germany was still beaming today over his victory of a third term in Sunday's first all-German elections in 58 years. But Kohl and his center-right coalition face a long and daunting list of problems, many of which threaten to undermine the confidence German voters expressed in their government.

Many of the thorniest aspects of German unification were put off until after the election and must now be dealt with. Decisions loom on such issues as the argument over whether the government should be based in Bonn or Berlin to the emotional debate over abortion, which is legal in eastern Germany but largely prohibited in the west.

Other consequences of blending the two Germanys are just now building to the boiling point. Unemployment in the east is soaring as industries collapse, unable to compete, and Western investment there is lagging well behind expectations because companies are reluctant to pump money into a society burdened by a backward infrastructure and a Communist work ethic.

The soaring cost of unification is expected to dominate the German political scene. After running a surplus last year, Germany will amass a $67 billion deficit this year and will go even deeper into the red in 1991. Karl Otto Poehl, chairman of the Bundesbank, the country's central bank, tonight said the rising deficit was threatening the stability of the German mark.

Economic analysts said today that Kohl can no longer choose among tax increases, deficit spending and budget cuts as he fashions a unification payment plan. Rather, they said, he will have to use all three measures. The costs are so high that, according to government sources, the German Finance Ministry is now planning to sell off at least portions of Lufthansa German Airlines, of which the government is majority owner, and Telekom, the government telecommunications monopoly.

Although Kohl maintained throughout the campaign that taxes will not be increased to pay for unity, he began hinting last month that "surcharges" might be necessary to clean up the environment.

"People are quite realistic," said Stephanie Wahl, a political analyst at the Institute for Economic and Social Policy in Bonn. "They don't believe at all what Kohl's been saying about taxes, but they also don't hold it against him. They figure that's politics."

The debate over how to pay for unification -- the massive costs of shutting down industries in the east that were propped up by East Germany's Communist rulers, rebuilding the defunct country's infrastructure, cleaning up four decades of ecological neglect and supporting millions of unemployed citizens -- began giving Kohl trouble on the very first day after the vote.

The Free Democrats, the centrist party of Foreign Minister Hans-Dietrich Genscher, were the big winners Sunday, receiving 11 percent of the vote, their best showing ever. The party is the traditional kingmaker of German politics, usually holding the crucial support the larger parties need to put together a parliamentary majority.

Today Genscher's party flexed its muscles, threatening not to remain in Kohl's coalition unless he drops his opposition to the Free Democrats' plan to boost investment in eastern Germany by keeping top tax rates lower there than in the west.

"We're not going to be faint-hearted and shy," Free Democratic Chairman Otto Lambsdorff said.

Editorials in German newspapers today said Sunday's vote was a bigger victory for the Free Democrats than for Kohl, whose Christian Democrats drew about the same level of support -- 44 percent -- they did in the last West German election in 1987.

Although some analysts believe it will take five years, a decade or more to bring the standard of living in the east up to the western level, others share Kohl's optimism.

"In another six months, everyone will realize there will be another economic miracle in ex-East Germany," said Werner Kaltefleiter, director of the Institute of Political Science in Kiel. "The infrastructure is in unbelievably bad shape, and that will take a long time to fix, but the investment will come anyway because there is money to be made there."

German stocks and bonds gained today, but analysts attributed the good performance more to optimism over the Persian Gulf crisis than to the reelection of Kohl's coalition.

German participation in the alliance against Iraq is only the most pressing facet of a broad debate over the future global role of Germany, which now has Europe's largest economy. Earlier this fall, when Germany felt strong pressure from the United States and its allies to join the effort against Iraq, Kohl belatedly came up with $2.2 billion but said the country's constitution would not allow German troops to go to the gulf.

Kohl promised then to push for a constitutional change giving the German military greater latitude. But broad popular opposition to any German role in the gulf led most politicians to drop the subject.

Now it is back. Asked today whether German troops might join others in the gulf in the coming months, Kohl said, "For the moment, I don't see this situation."

"Kohl committed himself to a constitutional change, but that doesn't mean he'll be able to get the two-thirds majority he needs for it," Wahl said.

"Sure, the public is opposed to sending the military, but we can't just take the good things about being a real sovereign state without accepting the responsibilities too. It's like a growing child; we can't play in the sandbox anymore."

Kohl can also expect opposition to increase as the bill mounts for the new responsibilities Germany is taking on throughout Eastern Europe and the Soviet Union.

Germany already has committed more than $13 billion in aid to Moscow, and although Germans reacted generously last week to a nationwide appeal for food and other help for the Soviet Union, politicians of all parties are bracing for an inevitable reaction against the country's expanding role as banker to less affluent nations.

Kohl's advisers believe that Germany must do whatever it can to help the Soviets and other reforming East European governments to prevent another wave of immigration, which would be extremely unpopular in a country already worried about unemployment.