To President Reagan, it means having "the courage to stand behind those who continue to put their lives on the line for democracy in Nicaragua." But to Rep. Lee H. Hamilton (D-Ind.), it means that the Central American "peace process would come to a halt."

With these divergent arguments, Reagan and leaders of the Democratic opposition in Congress yesterday outlined their strategies for the political warfare that will fill the next two weeks, ending Feb. 3 and 4 in what could finally be definitive congressional votes on continuing military aid to Nicaragua's contra rebels.

Supporting the contras' guerrilla struggle against Nicaragua's Marxist Sandinista government has been the most persistently controversial foreign policy issue of Reagan's seven years in office. No other policy has evoked such fervent backing from Reagan and his most ideologically conservative supporters and such heated opposition from Democratic liberals.

So deep has been the president's commitment to the contras that when Congress did decree a lengthy halt to military aid, his administration became embroiled in the apparently illegal, covert program of continuing assistance that eventually erupted into the Iran-contra affair. Yet, while last summer's congressional inquiry into the affair appeared to doom further contra aid, the administration somehow has kept the program sufficiently intact, and now appears to have at least a 50-50 chance of surviving yet another challenge by its opponents.

Administration officials said that renewing the aid will give the United States "an insurance policy" to force Nicaragua's Sandinista government to move toward democratization, while opponents said, as Hamilton put it yesterday, more aid would doom the regional peace process and cause "an escalation of war, with results we could neither predict nor control."

In a demonstration of his unrelenting position, Reagan yesterday formally notified Congress that failure to achieve a cease-fire in Nicaragua is due to "lack of good faith efforts" by the Sandinistas and that he therefore has ordered resumed shipments of military aid to the contras. He did that under an agreement with Congress that called for a brief pause in shipments already approved and in the supply pipeline but that left resumption to the president's discretion.

Under an agreement struck last month between the White House and Congress, Reagan will submit a new aid request to be voted on by the House Feb. 3 and the Senate Feb. 4. If both chambers defeat the request, the president will be barred by congressional rules from again seeking contra aid during fiscal 1988, which ends Sept. 30, and the program of U.S. support that has caused so much controversy for six years probably would die with the end of his presidency.

Spokesmen for both sides agree that this latest, and perhaps decisive round in the fight over contra aid will be determined by 30 to 50 potential swing votes in the House and roughly half a dozen in the Senate.

They also agree that the direction ultimately taken by the undecideds will depend on their perception of how hard Nicaraguan President Daniel Ortega works in the next two weeks to implement the promises he made last weekend at a meeting of the five presidents who signed the Central America peace agreement last Aug. 7.

However, even with Ortega in a potentially pivotal position to determine the outcome, both sides made clear yesterday that they will spare no effort to try to influence wavering members' perceptions of Ortega and his Marxist government.

"This really is a gut issue for the president," Hamilton, one of five House Democrats who conferred with Ortega during the Central American summit in San Jose, Costa Rica, told a breakfast meeting with reporters. "As we approach the vote, the administration will pull out every stop."

Reagan, speaking to senior administration officials a few hours later, declared that support of the contras is necessary to keep pressure on the Sandinistas, and he emotionally vowed to ensure that this final year of his presidency will be "the year that the United States will strongly affirm that democracy, not communism, is the future of Central America."

In effect, both were giving shorthand descriptions of the arguments that the two sides will use in the lobbying, cajoling and arm-twisting leading up to the votes that currently seem too close to call in light of the weekend developments. Ortega, under heavy pressure from the other presidents and warned by the visiting Democrats that Congress was watching him closely, promised several concessions, including lifting the state of the siege in Nicaragua and beginning face-to-face talks with the contras.

Administration officials reaffirmed yesterday that they will rely primarily on the "insurance policy" analogy in responding to Ortega. They plan to contend that the Sandinistas have made similar promises in the past only to renege on them later, that any liberalization they might permit in the coming days can easily be reversed after they achieve their goal of defeating contra aid and, if that happens, Congress and the American public might find it too late to revive a contra insurgency movement that has been starved too long for weapons and other supplies.

The officials said Reagan is to reiterate the urgency of renewed contra support in his State of the Union address next Monday night and to follow it Tuesday by formally making the aid request, whose size and scope is still under debate in the administration.

They added that current plans call for Secretary of State George P. Shultz to carry the request to Capitol Hill and testify for it before both chambers. In the ensuing week, the officials said, Shultz and Reagan's national security adviser, Lt. Gen. Colin L. Powell, are scheduled to lobby intensively with undecided members. The officials said Reagan is prepared to back up their efforts with public statements, appeals to groups able to put pressure on lawmakers and face-to-face White House meetings with members whose votes seem winnable.

The State Department was quick to point out that a Sandinista campaign of detaining domestic political opponents that began Saturday was continuing yesterday, and the officials argued that such actions show little sign of a Sandinista commitment to the democratization principles of the peace plan.

The Democrats' countering strategy was described to reporters in a joint appearance by Hamilton, Rep. Tony Coelho (Calif.), the House majority whip, and Rep. Matthew F. McHugh (N.Y.), another member of the delegation that went to San Jose last weekend.

Coelho, the Democrats' chief vote-counter, acknowledged that undecided votes in both chambers will be influenced heavily by what Ortega does to redeem his weekend promises.

"It is by no means a risk-free strategy," said Hamilton, who was cochairman of a special committee that investigated the Iran-contra affair last summer. But, Hamilton added, he agrees with Costa Rican President Oscar Arias, principal author of the peace plan, that Congress should "take a risk for peace."