Weighing budget options.

President Reagan today begins a second consecutive week of poring over a black notebook filled with budget-cutting options. This week he is expected to complete his review of potential cuts by turning to the most controversial pages in his briefing book - those dealing with defense spending.

The question of whether to trim planned increases in defense spending has sharply divided the administration. Defense Secretary Caspar W. Weinberger opposes any reduction. Administration economic officials, including Treasury Secretary Donald T. Regan and Office of Management and Budget Director David A. Stockman, as well as Republican congressional leaders, favor the inclusion of military spending in any attempt to hold the line on spending.

''If we are going to attack the deficit we can't set aside defense spending, '' newly elected Senate majority leader Bob Dole (R) Kansas said Sunday on NBC's Meet The Press. Senator Dole said defense spending reductions of $30 billion to government spending and cuts elsewhere.

At the moment, the President's budget strategy seems to center on finding a way to freeze fiscal 1986 spending at the $835 billion level now projected for 1985. The freeze would exclude interest on the national debt. And it would represent a cut of about $45 billion over spending that would occur in 1986 if current government services were continued unchanged.

The freeze strategy, which White House spokesman Larry Speakes cautions is still only a ''possibility,'' is being designed to appeal to Republican members of Congress. They say that across-the-board sacrifices would be easier to sell politically than attempts to eliminate or gut 20 to 25 programs concentrated in the domestic area. Mr. Stockman presented such wholesale cuts as another option for reaching the administration's tentative goal of cutting the budget deficit to 4 percent of gross national product (GNP) in 1986, 3 percent of GNP in '87, and 2 percent of GNP - or about $100 billion - by '88. According to a recent internal adminstration estimate, the deficit for '86 is now projected at $206 billion.

Republican support in Congress for the President's budget plan is crucial because at the moment White House aides say Mr. Reagan plans to pursue a two-track strategy for dealing with congressional Democrats next year: confrontation on the budget and cooperation on tax reform.

Cooperation on taxes would be required because, ironically, the Treasury Department's tax-reform plan is getting rave reviews from many Democratic economists. At the same time, the tax plan is being attacked by traditional GOP allies such as business and is getting the cold shoulder from Republican congressional leaders.

''I sort of like the tax code the way it is,'' Senate Finance Committee Chairman-elect Bob Packwood (R) of Oregon told the Washington Post last week. He added that he opposed drafting any major tax changes next year.

The adminstration hopes to move a tax-reform plan and budget cuts through the Congress next year on separate tracks. But ''deficit reduction has to come first ,'' Secretary Regan said Sunday on ABC's This Week with David Brinkley.

Administration aides and outside economists all caution that for various reasons, spending on all government programs cannot be frozen and that reaching the administration's budget-cutting targets will still require deep reductions in some programs or elimination of others.

Some limits on a spending freeze are technical. For example, interest on the debt, which in fiscal 1985 is expected to hit $133 billion, must be paid in full. And as new retirees become eligible for social security, they must be sent checks.

Other cracks in a general freeze are politically motivated. For instance, in this year's election campaign, President Reagan and Walter Mondale promised not to reduce the size of the checks going to current social security recipients.

''You don't get much'' in the way of budget savings from a freeze, says Robert Gough, senior vice-president of Data Resources Inc., a forecasting firm. ''It is not a way out of the (deficit) problem.''

Freezing domestic programs alone, to the extent technically possible, would produce savings of roughly $20 billion if defense were included, or maybe $10 to of Wharton Econometic Forecasting Associates. ''There is no way you can get $40 billion to $50 billion from a modified freeze,'' he says. Administration officials admit as much.

Among the programs said to be vulnerable to cuts are medicaid, federal housing assistance, federal salary increases, grants to local governments, and the Export-Import Bank.

Despite its limitations, ''there is a lot of support in Congress'' for the freeze concept, Senator Dole said Friday. He has argued for a freeze that would include defense.

Unless defense is part of the President's budget-cut package, ''I don't think we can get the votes'' needed to trim $45 billion from the deficit, Senator Packwood said Sunday. Secretary Regan said he did not think the President had made a final decision on defense spending reductions.

Democrats have already indicated that they will resist the President's current plan to bundle all proposed cuts into one bill for an up-or-down vote. ''We would certainly fight that,'' House Ways and Means Chairman Dan Rostenkowski (D) of Illinois said Sunday. He added that tax reform could be coupled with a measure that also raised taxes and cut spending.- 30 -