Reelected presidents face a choice of conserving personal popularity or investing it in causes that mean the most to them. In determining his national-security agenda for a second term, President Reagan has taken the latter course and dispelled any lingering doubts that he might become a stay-at-the-ranch chief executive.

For all of his firmness of purpose, Reagan is rarely an initiator of policy within his administration. But, at the onset of his second term, he has shown leadership on foreign policy issues that was largely lacking during his first four years. It is a display of involvement that contains promise and peril for his administration.

In meetings with advisers and congressional leaders, the president has said he will go to the mat for three priorities: the MX missile; the Strategic Defense Initiative, commonly called "Star Wars," and military aid for rebels opposing the leftist government of Nicaragua.

The MX missile has had more escapes than the Great Houdini, and it seems about to survive another time. Last week Reagan told key senators that the MX is essential to a "sound agreement in Geneva" when U.S.-Soviet arms-control negotiations resume this month.

The president's theological view that the MX is the path to arms control provokes skepticism among those who question the deterrent value of a missile that has first-strike capability and is to be deployed in relatively small numbers in vulnerable silos. But Reagan is well aware of congressional reluctance to undermine the U.S. negotiating position, and his advisers have maneuvered to bring the request for 21 additional MX missiles to a vote soon after negotiations begin. They are confident that what one of them calls "the glow of Geneva" will keep the MX alive.

The Strategic Defense Initiative, viewed strictly as a budget item rather than the ultimate defensive deterrent that Reagan envisions, is in even better shape. No, Reagan is not going to be given the full $3.7 billion he seeks for the SDI. But, if he receives $3 billion, which is likely, he will have doubled the budget for strategic-defense research at a critical time.

However, Reagan seems between a rock and a hard place in his up-front attempts to win congressional approval of funds for the anti-Sandinista rebels, whom he calls "freedom fighters" or "our brothers." Reagan's advisers say that the House is unlikely to permit a penny of aid for the rebels, even if the Great Communicator unleashes himself on national television.

On this issue, Reagan is truly demonstrating that he cares more about his causes than his popularity. During his first term, advocacy for a militant policy against Nicaragua came chiefly from Secretary of State Alexander M. Haig Jr., national security affairs adviser William P. Clark, U.N. Ambassador Jeane J. Kirkpatrick and Central Intelligence Agency Director William J. Casey.

Of this quartet, only Casey remains in the administration, and he is taking a back seat on Central America policy these days. Without prompting, Reagan is leading the charge and pushing a hard line that has carried him to the brink of calling for overthrow of the Managua government.

The tipoff came at a lunch Feb. 1 at which Reagan told his advisers he wanted to talk about Nicaragua in his radio speech the next day. Cooler heads persuaded the president to delay the speech and instead discuss the budget, but Reagan has been whipping up opposition to the Sandinistas ever since.

In his zeal, the president has constructed few lines of retreat. He has told aides he will not dispatch U.S. combat troops, a grasp of political reality neatly summarized by the State Department's chief Latin American expert, Langhorne A. (Tony) Motley, as: "The American people don't want another Cuba, and they also don't want another Vietnam."

This is a comforting recognition but not one that leaves much running room. Reagan has scorned Sandinista peace overtures as insincere while making it clear he is unwilling to tolerate a leftist government in Nicaragua. Blocked from waging war indirectly, he finds himself unwilling and unable to engage in direct military intervention.

Perhaps the only solution is that suggested by White House spokesman Larry Speakes last week when he said Sandinista peace rhetoric reflects the success of administration policies in the region. It was reminiscent of a famous proposal by the late senator George D. Aiken (R-Vt.), who once said the United States should declare victory in Vietnam and go home. Ultimately, this may be Reagan's best way out.

Reaganism of the Week: Speaking to the National Association of Independent Schools on Thursday, the president said, "Albert Einstein once said that 'science is nothing but everyday thinking carefully applied.' Well, that's easy for him to say."