President Reagan's hopes of rescuing his embattled $8.5 billion aircraft sale to Saudi Arabia suffered another severe blow yesterday when a potentially influential Democratic senator, Dale Bumpers of Arkansas, announced that he will vote against the deal.

Bumpers' decision brought to 51 -- a majority of the Senate -- the number of senators now on record as intending to vote against the sale of Airborne Warning and Control System (AWACS) planes when the package is considered by the Senate on Wednesday.

The House last week voted 301 to 111 against the deal. If the Senate follows suit, it will be the first time that Congress has exercised its prerogative of vetoing a major arms sale.

Bumpers' declaration also was important because the administration, which lobbied hard to win his support, had hoped that he might influence other undecided senators and some southern Democrats now counted as opponents into supporting the president.

Bumpers said Reagan telephoned him from Cancun, Mexico -- a last-minute bid for support that underscored the importance the White House attached to Bumpers' vote. But Bumpers had already released his statement.

The administration's failure to win over Bumpers deepened the growing sense on Capitol Hill that a solid majority against the sale now exists in the Senate and that Reagan can reverse the numbers only if he wins new concessions from the Saudis giving the United States greater control over the operation of the AWACS planes.

But, while Reagan met yesterday in Cancun with Saudi Crown Prince Fahd, the initial indications were that the Saudi government remains unwilling to modify its resistance to some form of joint control. As a result, even Republican sources in the Senate have been predicting that the last-ditch lobbying blitz planned by Reagan for next week will fail to turn up the votes he needs.

In addition to the 51 senators now on record as opposed, some of the remaining undecideds also are expected to vote against the sale. Some congressional sources now estimate that the final tally could see as many as 55 to 57 senators turning thumbs down on the deal.

In fact, the opposition has become so confident that Sen. Edward M. Kennedy (D-Mass.) yesterday urged Reagan to withdraw the package of AWACS planes and other aircraft equipment as a means of containing the damage to himself and to U.S.-Saudi relations.

"It is one of the most dangerous arms sales ever considered by our country," Kennedy said. "I therefore call on the president to withdraw the proposed AWACS sale to Saudi Arabia before the Senate votes."

Kennedy's proposal was endorsed by Sen. Alan Cranston (D-Calif.), a leader of the Senate opposition, who said that pulling back the sales package "would avoid a defeat for the president and a defeat for Saudi Arabia."

However, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), declaring that the battle "is still eminently winnable," said that he has not discussed the withdrawal option with the president.

The White House's lobbying strategy had been aimed at winning most of the undecideds and at inducing potential waverers in the opposition, especially freshmen Republicans and southern Democrats, to switch sides.

However, the drive to turn around some of the southern Democrats has been dealt a major setback by the decisions of Bumpers, Ernest F. Hollings (D-S.C.) and, most importantly, Minority Leader Robert C. Byrd (D-W.Va.) to oppose the sale. As a result, the administration's main targets in this category, Howell T. Heflin (D-Ala.), a declared opponent, and David L. Boren (D-Okla.), who has been undecided, now appear likely to go with the opposition.

Similarly, those freshmen Republicans the administration has been making its biggest effort to win -- Robert W. Kasten Jr. of Wisconsin, Slade Gorton of Washington and Mark Andrews of North Dakota -- have continued to insist on the need for a system of joint control greater than Reagan is able to deliver.

The administration still could switch some votes with the intensive lobbying push it intends to pursue right up until Wednesday's vote. But unless Reagan's talks with Fahd have armed the president with new ammunition that was not readily apparent last night, the almost unanimous opinion being expressed privately by congressional head-counters is that the effort will be too little and too late.