It is billed as a rally, but even in a city accustomed to protests and gatherings of all types, today's lunch-hour demonstration on the west front steps of the Capitol will be an unusual one.

For one matter, it's by invitation only.

Participants must produce a special pass, walk through a metal detector and hand over handbags and briefcases for searching before being allowed inside.

The restrictions and security are necessary, say the demonstration's organizers, because of another of the rally's distinctions--the keynote speaker is to be the president of the United States.

President Reagan, himself the target of small and large protest rallies in many of the cities he visits, is turning the tables today and leading a demonstration of his own. The invited throngs, expected to number between 3,000 and 5,000, will be able to hear Reagan speak for the balanced budget consitutional amendment.

The rally on the Capitol grounds is being organized with the help of the White House and to climax a half day of events orchestrated with an aim of positioning Reagan in the front of the movement for an amendment making it more difficult for Congress to produce unbalanced budgets.

The movement comes in the wake of a Reagan budget, now pending on the Hill, that has a record deficit in excess of $100 billion--an irony that is not lost on the balanced-budget amendment's opponents.

Sen. Alan Cranston (D-Calif.), who is leading the Senate fight against the proposal, contended yesterday that the president is "calling for a constitutional amendment to require him to stop doing what he is doing."

Cranston, appearing on "Meet the Press" (NBC, WRC), said the amendment "could paralyze our government" and would jeopardize the health of the economy, and he predicted that the amendment would ultimately bring the courts into the budget process.

But the leading Senate proponent of the amendment, Sen. Orrin G. Hatch (R-Utah), predicted on the same program that the amendment, which has 61 Senate co-sponsors and 220 in the House, would pass both houses.

In pre-rally events at the White House today, Reagan is formally to agree to be honorary chairman of the American Lobby, a newly formed group of conservative business, government and civic leaders that the White House helped organize to lobby for the balanced budget amendment.

After Reagan sees a delegation headed by Pepsico chairman Donald Kendall, the group will go to the State dining room and East Room where they will be joined by about 500 others to hear what are called "advocacy briefings" on the amendment by Treasury Secretary Donald T. Regan, Office of Management and Budget Director David A. Stockman and presidential counselor Edwin Meese III.

Similar briefings at the White House are planned on Tuesday for Reagan's Hispanic supporters, on the issue of Reagan's Caribbean Basin Initiative.

On Wednesday evening, another citizen's lobbying group in behalf of that initiative--legislation granting $350 million in assistance and trade and investment to the region--hope Reagan will attend a "gala" they have planned at the Organization of American States.

Both the balanced budget amendment and the Caribbean aid and investment package are at the top of Reagan's legislative agenda this year, White House chief of staff James A. Baker III said last week, but both initiatives have been overshadowed by the protracted battles over the budget in the last months.

Now, as presidential advisers test strategies to remove Reagan from the pitched election battles they anticipate over the failure of his economic program to spur recovery, they are seeking to identify him with issues aimed at the future.

After today's rally, some Democrats, labor leaders and senior citizen groups plan a counter-rally press conference on the east front of the Capitol.