Prime Minister Anker Jorgensen's new minority Social Democratic government faces two rapidly approaching decisions on military defense that could seriously undermine its commitment to restore Denmark's economic health.

As a member of the NATO alliance, Denmark must decide if it supports stationing in Western Europe new medium-range missiles that could strike into the Soviet Union. Jorgensen must also examine his two-year-old promise to President Carter to increase Denmark's defense budget to meet NATO's general 3 percent rise in defense budgets.

The situation is further complicated by the fact that some Danish politicians have been impressed by the arguments of a trio of Americans who are experts on arms control. The three are asking Denmark to seek a delay in the NATO decision to deploy the new missiles while a new offer by Soviet leader Leonid Brezhnev to cut Soviet arms in Europe is explored fully.

Danish diplomats already have agreed in principle with other NATO countries to approve in December deployment of the new nuclear missiles in Europe and then use the four-year lead time before they are ready for installation to explore with the Soviet Union the possibility of mutual missile reductions in Europe.

Now none of this is so certain. The missile deployment and defense budget decisions have been placed in doubt by a combination of factors that illustrate the squeeze East-West nuclear politics can put on a small, strategically located NATO nation that seeks both to deter attack from the nearby Soviet giant and to explore any genuine possibility for world disarmament.

Brezhnev's symbolic unilateral troop and tank reduction in East Germany and his offer to cut back on Soviet missiles if NATO decided in December not to deploy the United States' new Pershing and ground-launched Cruise missiles is being viewed here as just such a possibility, however remote and obviously self-serving.

The three Americans impressing some Danish politicians -- all former U.S. government disarmament experts -- spent three days in Copenhagen last month. Herbert Scoville, a former assistant director of the Arms Control and Disarmament Agency; Arthur M. Cox, a former European arms expert with the State Department and the Central Intelligence Agency; and Richard Barnett, a director of the Institute for Policy Studies in Washington are all opponents of deployment of new NATO nuclear missiles.

Sponsored by the Danish newspaper Information and by the United Nations Association, the Americans met with influential Danes to argue that introducing the new NATO missiles into Europe would, in Scoville's words, "signal a new level in the arms race . . . and put Europe in the front line of the U.S.-Soviet strategic battle."

The U.S. Embassy in Copenhagen, Scoville said, was "not very happy" with the visit of his unofficial delegation, "because it went against U.S. policy."

Government sources in Washington confirm that some officials dealing with the sensitive NATO missile issue were "burned up" over Scoville's activities. According to one source, the United States still expects the Danes to support a production if not deployment decision in December.

Following his return to Washington, Scoville said he told Danish officials "they should not be railroaded in December" into approving the new system.

For almost 20 years, the Soviets have had about 600 SS4 and SS5 intermediate-range missiles aimed at Western European targets. In the last two years, they have introduced a new, more accurate, mobile SS20 missile that carries three individually targeted warheads.

"It's unlikely they are going to scrap any of the 80 to 90 SS20 missiles they have aimed at Europe," Scoville said, "but we might be able to get rid of the old SS4s and SS5s."

According to knowledgeable Danish sources, the three Americans had a significant impact on the political debate in Denmark. Scoville "argued his points well and is regarded here as a serious man," one Dane said.

Their arguments aainst the new missile deployment were picked up during the election campaing by leaders of two smaller parties on the left while the leaders of two other smaller parties on the right declared that Denmark should not only approve installation of the missiles but allow them on Danish soil.

The two right-of-center parties, the tax-protest Progress Party and the splinter Center Democrats both suffered serious losses. Center Democrat leader Erhard Jakobsen attributed his party's setback to his urging that Denmark accept NATO nuclear weapons on its soil.

This has given courage to those in the sizable left wing of Jorgensen's own Social Democrats who oppose the new NATO missiles and any increase in Denmark's defense budget.

Prime Minister Jorgensen promised President Carter two years ago in Washington that Denmark would go along with the NATO-wide 3 percent spending increase if possible when drawing up a new four-year Danish defense plan.

Now Jorgensen's opponents within his party are arguing that cuts in government spending on social problems must be matched by defense spending reductions.

Jorgensen has decided to conduct a reevaluation of the Danish position on both the NATO missiles and the level of military spending in the four-year Danish defense plan, which is now under consideration.

Well-placed Danish sources still expect Jorgensen's government to support approval of deployment, so long as it is tied to a serious exploration of the Soviet offer of arms reduction.

But they also expect that at the December NATO defense ministers' meeting, where this decision is to be made, Denmark will watch to see what a country like the Netherlands does. If the Netherlands refuses to allow the new missiles to be installed on NATO bases on its soil or seeks a delay in the decision, Denmark may also decide to balk, these sources said.