The lengthy and bitter struggle over Texas International Airlines' bid to acquire Continental Airlines has moved finally to the desk of President Reagan, culminating eight months of legal and regulatory wrangling that has spanned the continent.

The president has until next Tuesday night to disapprove the contested takeover or let it go forward, as the Civil Aeronautics Board has unanimously recommended. His decision could come as early as today.

Although the White House has never vetoed an airline merger, industry observers note that the president and White House staffers have strong ties to California-based Continental and members of its board of directors. Board member Jack Wrather and Earle Jorgensen, whose wife Marion Jorgensen is on the board, both were members of the highly visible committee of longtime Reagan associates who made recommendations for Reagan's Cabinet and sub-cabinet appointments.

Since Texas International made its initial move in February to acquire the larger but financially weaker airline, the hotly contested takeover has been taken up, in one form or another, in at least one state and two federal courts, the regulatory agencies of three states, two federal agencies, the California legislature, Congress and the New York Stock Exchange.

There has also been intense lobbying, especially since the CAB sent its favorable decision to the White House in mid-August for the 60-day presidential review. Heading Texas International's efforts has been Stan Anderson, a former assistant secretary of state in the Nixon administration who served as a top transition official for the Reagan administration. Two of TI's lawyers with good Republican connections are John W. Barnum, former deputy secretary of transportation, and Calvin J. Collier, former Federal Trade Commission chairman and official of the Office of Management and Budget.

Among others, including some big hitters from the Carter administration, Continental has been aided by the efforts of former Central Intelligence Agency Director William E. Colby; Douglas Bennett, director of the White House peronnel office under President Ford; Joe Baroody, whose father started the American Enterprise Institute, considered the Republican think-tank; and his firm colleague, John Laxalt, brother of presidential confidant Sen. Paul Laxalt (R-Nev.).

Colby was hired by Continental to make the argument to the Defense Department that Texas International's takeover of Continental would jeopardize the nation's security and should be turned down.

A quirk in the law gives the president the authority to review mergers between airlines while an acquisition of an airline by a non-airline firm, such as Mobil Oil or Sears, Roebuck & Co., for instance, wouldn't have to go through the CAB and be forwarded to the White House. The president's authority to disapprove a merger between airlines is limited, however, to reasons of foreign policy and national security.

Continental is contending that its air services to the "strategically important" U.S. Trust Territory of Micronesia are jeopardized by the takeover, despite Texas International's written commitment to continue and even upgrade Continental's current service to Micronesia and a CAB-imposed provision on the merger that would make it tougher for TI to drop or reduce services than it is for Continental.

Continental's representations to officials of the South Pacific islands it serves -- that their service would be disrupted by the takeover -- resulted in a barrage of letters to Washington opposing the merger. This prompted TI to dispatch one of its officials to the islands last month to try to counter the claims.

Despite the resources of Texas Air Corp., TI's parent company, which has $80 million in cash, Continental has argued that a combined CO-TI would be forced to drop its South Pacific services because it would be financially unstable. TI countered, in a memorandum to the government, that "it simply defies logic for Continental to argue that its acquisition by a financially stronger carrier will cause Continental to be intolerably weak."

Of the two airlines, TI has the better recent financial past. The Houston-based airline is generally considered profitable despite a $4.5 million loss during the first half of 1981. It earned $41.4 million in 1979 and $4.7 million in 1980.