The 99th Congress will convene officially Thursday to face an agenda packed with potential problems for President Reagan as he prepares for his second inauguration.

Budget deficits in the $200 billion range are expected to dominate debate, with pressure already mounting for deeper cuts in defense spending than Reagan wants and for modification of his latest proposals for cutbacks in social welfare spending.

Early votes are expected on the controversial MX missile and on resumption of aid to anti-government guerrillas in Nicaragua, followed by politically prickly struggles over over farm, housing, feeding and environmental programs, most of which have budgetary impact that will ensnarl them in the deficit-reduction effort.

There will be a major push for tax simplification, including income tax rate reductions financed by the elimination of many popular deductions. There is little talk as yet of a general tax increase, although it is being held as a "last resort" solution if spending cuts fail to make a big enough dent in the budget deficit.

Even though Congress may not get down to real business until after Reagan is inaugurated Jan. 21, warning flares have been fired from Capitol Hill -- mostly from behind Republican lines.

They indicate that the differences separating the conservative White House and more centrist Congress during the later years of Reagan's first term remain, and have perhaps intensified.

While Reagan is still defining the terms of the debate on Capitol Hill, emphasizing the reduction of government at home while rearming to strengthen the country's posture abroad, Congress is having second thoughts about some specific initiatives, ranging from the MX missile and Nicaragua to the balance between spending for defense and for social welfare.

Moreover, although there are few new issues on the horizon, enough old ones remain to make this one of the busiest and most contentious sessions in recent years.

Pressure for tax simplification, as proposed by Treasury Secretary Donald T. Regan and lawmakers of both parties, has gained momentum and is likely to be seriously considered for the first time, although prospects for speedy enactment are dim.

Many major programs will expire this year, including farm price supports, housing subsidies, food stamps and other nutrition aid, and a wide variety of laws aimed at protecting the environment, including the "Superfund" for toxic waste cleanup. Problems affecting long-delayed highway and water-project allocations also await solution.

Issues left over from previous years include the nomination of White House chief of staff Edwin Meese III as attorney general, banking deregulation, ratification of an international anti-genocide treaty, and legislation overturning a Supreme Court decision that narrowed the scope of federal civil rights laws.

There will be pressure for increased aid to economically troubled Israel, along with another anticipated fight over new arms sales to Arab countries. Support is mounting for more famine relief for Africa as well as sanctions against the minority government in South Africa.

Internally, both houses are grappling with reforms, including a possible streamlining of their budget and intelligence oversight operations, all of which could affect Reagan's program and his relations with Congress.

In contrast with the easy victories that he won from a compliant Congress four years ago, Reagan faces trench warfare almost from the start of his second term in nearly every major category of legislative issue, foreign as well as domestic.

Anticipated early votes on resuming production of MX missiles and aid to the Nicaraguan "contras," both of which were temporarily blocked late last year, could provide shaky grounds for trial runs of administration strength. The administration faces uphill fights on both issues and risks loss of important momentum on the Hill if the president chooses to fight and then loses on one or both counts.

Moreover, there have been stern warnings from congressional leaders, especially Republicans, that Reagan could lose the battle of the budget for this year, and perhaps for the rest of his second term, unless he moves farther toward a defense spending compromise.

More specifically, they say, he risks losing the domestic spending cuts he wants -- and may invite a tax increase that he doesn't want -- unless he agrees to more restraint in defense spending.

Reagan comes to the fray with his hand considerably strengthened by a landslide reelection victory, prosperity at home and movement toward arms-control talks abroad. In Congress, his party expanded its modest ranks in the House and retained control of the Senate despite a two-seat loss, while the Democrats appear preoccupied with their own soul-searching.

But Reagan is a lame-duck president, facing the problems that often hobble a chief executive in his last term. Many lawmakers have said he probably has only the first few months of his term to make any major breakthroughs, which puts a premium on swift action and casts doubt over prospects for such long-term projects as tax simplification.

Moreover, Republican gains in the House and Democratic gains in the Senate have brought the two houses closer philosophically, which some lawmakers believe could mean more cohesion on Capitol Hill in scraps with the White House.

Perhaps even more important, Senate Republicans, once the linchpin of administration strength in Congress, have shown an independence and feistiness in their choice of new leaders, posing problems for the White House unless GOP lawmakers are given a hand in shaping administration policy.

With Democrats watching quietly from the sidelines, Republicans have taken the lead in calling for scrapping the MX missile, keeping the current embargo on aid to Nicaraguan "contra" guerrillas and imposing a budget freeze that would include defense as well as domestic spending.

The MX missile, for instance, is believed by some to be in more trouble in the Senate than it is in the House.

More significantly, Senate Republican leaders, under the direction of incoming Majority Leader Robert J. Dole (R-Kan.) and Budget Committee Chairman Pete V. Domenici (R-N.M.), are charting an independent course on the budget.

They are preparing an alternative to Reagan's anticipated budget for fiscal 1986 that would more severely scale back future deficits by an across-the-board freeze including defense as well as inflation adjustments for Social Security, which both Reagan and the Democrats are skittish about. Only programs targeted at the poor, which Reagan has cut and proposes to cut again in some cases, would be exempt.

Leaders in both chambers have expressed reluctance to push ahead with tax simplification if it gets in the way of deficit reduction. Dole has made deficit reduction his foremost priority, and House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) has balked at pushing a simplification plan that does not help produce new revenues to reduce deficits.

In contrast to previous years, when even Democrats went along with substantial increases in defense spending, this year many Republicans are talking about freezing Pentagon outlays, followed by modest increases starting next year. Such an approach has been rejected by Reagan and Defense Secretary Caspar W. Weinberger, who seek an increase of about 11 percent a year, or more than 6 percent after accounting for inflation.

A defense freeze would probably force a cutback in the growth of weaponry, which was largely untouched in earlier years. This could further jeopardize the MX and cast a cloud over other expensive initiatives, including Reagan's proposed "Star Wars" technology for defense against missiles in space.

Offsetting this, however, is the argument that the administration is making to the effect that weapons programs should not be blocked just as the United States is entering arms-control negotiations with the Soviets. This could be the ace in the hole for the MX, at least for this year.

Reagan also has an advantage in the MX and Nicaragua debates in that he can control the timing of the congressional votes because they are contingent on requests from the White House. But release of the funds requires positive votes from both houses, giving each chamber what amounts to a veto.