The Hague — Rudolph Lubbers, sworn in early this month as the Netherland's youngest prime minister, heads a new center-right government faced with repairing a country wracked by skyrocketing unemployment (now 12.3 percent), a massive budget deficit ($10.7 billion), and declining industrial productivity.
Already the new Dutch government has come under fire for its Nov. 22 announcement of tough spending cuts and a public sector wage freeze. Socialist unions called ''massive and lengthy'' strikes against the proposals. Trains and buses in much of the country were idle as well last week to protest the anticipated freeze.
Mr. Lubbers' toughest task, however, may be to handle successfully the very issue that has eluded resolution by successive Dutch governments for nearly three years: whether to accept the deployment of new US nuclear missiles on Dutch soil if the long-running US-Soviet arms talks in Geneva fail.
''The problem may make or break his government,'' a political insider said.
Under a plan agreed to in principle within NATO in December 1979, the Netherlands is scheduled to receive 48 of the 572 US-made cruise and Pershing II nuclear missiles to be deployed in several West European countries beginning next year. Several Dutch governments - under strong pressure from the country's massive antinuclear movement - have said that final acceptance is conditional on a lack of progress at the Geneva talks.
Political observers say that by awarding the defense and foreign affairs posts in his 14-member Cabinet to fellow Christian Democrats, Mr. Lubbers plans to keep a firm personal grip on the controversial missile issue as well as on other sensitive political matters.
The new government's draft program - negotiated by the Christian Democrats and their coalition partners, the right-wing Liberals - takes a markedly cautious approach to the issue, saying the country should continue to prepare for deployment ''in order to leave the door open for the possibility that deployment will take place . . . without making a decision in principle at this moment.''
Analysts say that Lubbers is likely to take an ambivalent line on the missile question for many months to come - certainly more ambivalent than did his predecessor, Andries Van Agt, also a Christian Democrat.
During his three premierships in the last five years, Van Agt had moved increasingly to the right within his party on the missile issue, coming out in favor of deployment while the party continued to remain noncommittal, fearing voter retaliation.
If anything, Lubbers - who reportedly amassed a personal fortune in business before entering politics and rising to economics minister in 1973 - leans to the political left, according to most observers. ''But whatever decision he finally takes,'' one said, ''he will have built a broad-based consensus before standing on it.''
Under the Dutch system, however, the final decision on whether the new US nuclear weapons will be stationed in the Netherlands will not be left to Lubbers alone. The issue will have to be put to a vote in Parliament, and although the Christian Democrats and the Liberals together have a clear majority in the new Parliament, holding a combined total of 81 of the 150 seats, the vote could be close.
''Parliament will never approve the deployment of new nuclear missiles in the Netherlands,'' one source said. ''There's just too much public opposition to it.''
That could become even more true as the date for deploying the new weapons draws near and the antinuclear movement - dormant in recent months - begins to mobilize public opinion again. Siding with the movement as well will be the Socialist Party - still the largest single party in the country following the general elections in September.
''A decision in favor of stationing the missiles here,'' a Dutch peace movement leader said recently, ''would bring hundreds of thousands of demonstrators into the streets.''