To Secretary of State Alexander M. Haig Jr., it is a matter that could mean the difference between war and peace. And the chairman of the Senate Armed Services News Analysis News Analysis Committee, John G. Tower (R-Tex.), says he is appalled that so many other senators are reluctant to do what Haig and President Reagan want.

The anxiety voiced last week by Tower, one of Capitol Hill's most astute nose-counters, is perhaps the clearest sign that the administration's high-priority plan to sell sophisticated radar planes to Saudi Arabia is in serious danger of being derailed by a thumbs-down vote of the Senate.

As of now, a thin but distinct majority of the Senate seems inclined to go against the administration's wishes. And the impending struggle to turn the numbers around already has marked the controversy over the Airborne Warning and Control System (AWACS) planes as the most emotional foreign policy debate to buffet Congress since the battle four years ago over the Panama Canal treaties.

It's a debate whose implications go far beyond arguments about whether there is a military advantage for the United States in selling AWACS to the Saudis. At stake, in the administration's view, is the future of its grand strategy for dealing with the Middle East and the credibility of Reagan's ability to conduct American foreign policy.

Even those who reject the sky-is-falling tone of the administration's rhetoric concede that the outcome will have far-reaching implications for future U.S. relations with Saudi Arabia, America's principal foreign oil supplier, and with Israel, which opposes the AWACS sale as a threat to its security.

At issue is a proposed $8.5 billion sale that would provide Saudi Arabia with five AWACS planes, plus range-enhancing fuel tanks and multi-ejection bomb racks for the 62 F15 fighter-bombers purchased by the Saudis during the Carter administration years, air-refueling tankers and air-to-air Sidewinder missiles.

To the administration, the deal provides not just an opportunity to cement the special U.S. relationship with the Saudis. In testimony before the Senate Foreign Relations Committee last Thursday, Haig called it "the cornerstone of the president's policy to strengthen the strategic environment of the Middle East."

That was a reference to the administration's much-touted hopes for knitting together a "strategic consensus" to assist friendly Mideast countries to guard against the possibility of Soviet encroachment in the region.

U.S. policymakers view the Saudi sale as simultaneously binding Saudi Arabia closer to the West, allowing it to better ward off threats to the Persian Gulf oil fields by Soviet proxies and pre-positioning in the gulf area a large stockpile of advanced American weaponry that U.S. forces theoretically could take over and use in the event of a broader-scale crisis.

The sale can be blocked if both houses of Congress vote against it within 30 days after they are notified formally of the administration's intention. The administration, aware of this potential pitfall, sought to defuse the expected outcry from Israel by working out a series of still-secret agreements with the Saudis that U.S. officials contend will provide adequate safeguards against the equipment being used against Israel in a future Arab-Israeli conflict.

As a result, when the administration decided in March to go ahead with the AWACS part of the deal, it was confident that it could skirt any congressional obstacles. White House strategists conceded that the Democratic House was likely to vote against the sale, but they reasoned that the Republican-controlled and presumably more sympathetic Senate would back the president.

So far, though, it hasn't been working out that way. Instead, on the heels of Haig's almost impassioned testimony to the Foreign Relations Committee on Thursday, 50 senators, led by Bob Packwood (R-Ore.), unveiled a resolution announcing that their current intention is to vote against the sale. An estimated six or seven other senators, who didn't sign the resolution, also are known to be leaning against the administration.

Although the battle is far from decided, all indications are that the administration, if it is to reverse the tide, will have to invest in an incredible amount of coaxing, arm-twisting and horsetrading between now and the end of October, when the Senate is to vote on the issue.

Even then, many congressional sources insist, the effort is unlikely to produce the desired result unless the administration reshuffles the package to include compromises it insists are unacceptable to it and the Saudi government.

Interviews with several senators and congressional aides indicate that the administration's dilemma is due to its failure to heed earlier warnings from Capitol Hill that there were strong reservations about many parts of the package and, instead of trying to shore up the weak points in its case, plunging ahead with arguments that many senators find unconvincing and inadequate to allay their respective concerns.

For example, the argument about the credibility of Reagan's ability to provide strong leadership for American foreign policy has met with a tepid response from Democrats, who recall that the same plea was made on behalf of then-President Carter during the Panama Canal debate.

Yet, they point out, that didn't prevent Reagan from acting as spiritual leader of the forces opposing the canal treaties or Republican foreign policy hawks now supporting the AWACS sale from voting against the treaties.

Similarly, the Senate's strongly pro-Israel members have capitalized on what they regard as the administration's attempts to hint that promises of increased U.S.-Israeli military cooperation might be reassessed if Prime Minister Menachem Begin doesn't check his public opposition to the sale and the implying by some administration officials that the "Jewish lobby" has too much influence in Congress.

Several Senate sources said the administration made bad tactical blunders when Max Friedersdorf, the chief White House lobbyist, sent lawmakers a letter containing news articles critical of Begin and Israel, a 6------------------------------------------------------- move that prompted an official protest from the Israeli Embassy here, and when unidentified White House sources reportedly ascribed Packwood's opposition to his role as chief fund-raiser for Senate Republicans and his fear of alienating Jewish contributors.

But, in the view of many congressional sources, the administration's biggest miscalculation was in assuming that Republican conservatives automatically would be bewitched by the "strategic consensus" concept with its overtly anti-Soviet implications.

Instead, a small but potentially decisive group of conservatives has taken the line that this strategy poses the same dangers that arose when the United States loaded the late shah of Iran with sophisticated military equipment, only to see him overthrown by virulently anti-American forces.

These senators, concerned that the same thing could happen in Saudi Arabia, have been insisting that highly secret, advanced technology such as the AWACS should not be put in the hands of what they regard as an unstable regime unless the United States retains a strong measure of control over its protection and use.

In fact, this question of control appears to be emerging as the issue over which the administration will win or lose the AWACS fight. During the last few days, there has been a rush by many senators to embrace the suggestion by Sen. John Glenn (D-Ohio) that the AWACS not be sold but leased to the Saudis under a joint-command arrangement.

Several of those senators who signed the Packwood resolution and who now are targets of administration pressures to switch have said publicly that they will do so only in exchange for an arrangement along the lines proposed by Glenn.

However, such ideas have been rejected by the Saudis as an infringement of their sovereignty, and administration officials insist there is no hope of getting the Saudi government to relent.

For the moment, the administration is sticking with the position that the agreements it has made with the Saudis provide adequate safeguard controls and that a majority of senators will reach the same conclusion once they have been briefed fully on the details.

But there's a lot of skepticism, expressed publicly on Capitol Hill and privately in the administration, whether that strategy, even if it eventually means making public the details of the secret agreements, will give the administration the push it needs to carry the AWACS deal successfully through the steep climb confronting it.