The Hotel Galvez in nearby Galveston is a massive pile of weather-beaten stone that has stood like a brooding presence beside the Gulf of Mexico for more than 60 years.

The hotel is old and crumbling now. But in its time, the manager recalls, it was an institution in Texas politics - "a place where Presidents stayed and where every politican who came here to court votes made his headquarters."

On Thursday evening, a touch of that old spirit returned to the Galvez. For a few hours the hotel echoed with the excitement of political debate, stirred by a barnstorming campaigner making a pitch to the voters.

It wasn't a debate about taxes or zoning or any of the other local issues that might normally draw people away from their TV sets. Nor did the barnstormer fit the larger-than-life image of a Texas-style politician.

Instead, up on the speaker's platform was a soft-spoken, diminutive young woman named Sally Shelton, who is neither a professional politican nor a seeker after elected office.

She is a middle-management executive of the State Department with the rank of deputy assistant secretary. What brought her to Galveston was the growing national controversy about the Carter administration's proposal to surrender U.S. control over the Panama Canal by the end of the century.

Shelton is one of several State Department officers who are being sent around the country on an increasingly high-priority mission. The department, concerned about charges that its personnel are being used for political purposes, delicately refers to their task as "educating and informing the public."

But their purpose is quite clear: to counteract those forces seeking to prevent the administration's canal treaties from winning the required two-thirds Senate vote.

It's an uphill fight, as Shelton learned on a three-day whirl through the Houston area last week.

The canal arouses special passions in Texas, where military bases and American Legion halls abound, doctrinaire military ideas are influential and Gulf Coast shipping relies on the canal to reach Pacific markets - a matter of real dollars-and-cents concern.

Republican Sen. John Tower is counted among those opposing the canal pacts. Democrat Lloyd Bentsen is still uncommitted, and because his ultimate decision could sway the votes of four or five other senators. Bentsen is one of the biggest targets of the orchestrated letter-writing campaigns and other tactics being employed by anti-treaty forces.

The situation was made clear to Shelton immediately. She called on an old friend, Houston Mayor Fred Hofheinz, and he told her bluntly:

"The treaties have no constitutency in Texas. Although most people aren't that concerned about them, there is a very vocal and very dedicated minority of antis that is. On the other side, there's no equally dedicated pro minority to offset the right. If I were Lloyd Bentsen, I'd have to think very hard about whether I wanted to be a statesman or whether I wanted to get reelected" when the treaty vote comes up.

Shelton was to hear echoes of his warning wherever she went. The message came across with particular clarity in Galveston, where she encountered an overflow audience and a cross-section of the fears and suspicions that the treaties arouse.

There was the prejudice of a lawyer who asserted, "The Panamanians grow great coffee, but they can't run he canal."

There was the anxiety of a port worker who asked: "What does the government plan to do with the population of the Gulf Coast? Put us on relief?"

And there was jingoism of an architect who evoked cheers when he pointed a finger at Shelton and shouted:

"You bureaucrats in Washington are only interested in advancing your careers by giving things to other countries. Someday I'd like to see one of you put the interests of America first."

Mostly though, she found ignorance. Despite all the discussion by press and Congress, the questions asked of Shelton reflected only the haziest notions of what the treaties say.

The administration, which believes that most of the opposition is rooted in a lack of information and that public opinion can be changed through an education campaign, has called upon big names like the two U.S. treaty negotiators, Ellsworth Bunker and Sol M. Linowitz, and the normally anonymous young Foreign Service officers like Shelton who can bring special expertise to the assignment.

The department tries to exercise care in matching speakers to audiences. One official points out. "You're not going to accomplish much if you send someone with two last names and a Harvard accent to talk to an American Legion post in Alabama."

Shelton, for example, was asked to take the Houston assignment for several reasons.

Her job in the department's Bureau of InterAmerican Affairs is to ride herd on U.S. diplomatic activities in the Caribbean and Central American area that includes Panama. She is a native Texan, whose family lives in Houston. Before joining the State Department last summer, she spent six years as a legislative aide to Bentsen, working on foreign policy matters, and she is acquainted with many state political and business leaders.

"I'm not here to try and sell anything," she stressed wherever she went, but she operated on a timed-to-the-minute schedule that made her look like an election campaigner.

From dawn to midnight she delivered set-piece speeches before big audiences, hunddled in the richly paneled private clubrooms of Houston's business elite, taped local TV talk shows, sipped coffee witha young Mexican-American political leader in a University of Houston cafeteria.

Through it all, Shelton kept her sell soft, quietly but tirelessly repeating her message that the treaties will further foreign policy interests without harming military or economic strength. She gracefully turned aside the taunts of hostile questioners and usually managed to give the impression that she was responding for the first time to a question, though dozens of other people already had asked it.

Occasionally she stumbled, tripping on a fact or giving a response that audiences found confusing. More than once she was forced to say, "I can't answer that. But if youll give me your name and address, I'll see that the information is sent to you."

By the end of the tour, Shelton confessed, she had no idea about what, if anything, her efforts had accomplished. Perhaps the best answer was an equivocal one, and it too came in Galveston.

About 350 people assembled in the peeling gilt of the Galvez's once grand ballroom ro hear Shelton. One member of the audience, retired Rear Adm. John Smith, who heads a local Merchant Marine Training Academy, noted:

"It may not look like much, but this is really a sign of the tremendous interest here in the canal issue. Normally, you'd be lucky to get 15 people to a discussion of foreign affairs in this town."

The session went on for five hours. At the end, the audience was asked to vote on the treaties. When the ballots were counted, they showed 85 in favor and 138 against.

From Shelton's point of view, that wasn't encouraging. But roughly 100 of those present didn't vote. Most said it was because they were undecided. Some added that they had come to the meeting opposed to the treaties but were now having second thoughts because of what they heard.

As Robert Handy, the council chairman, noted, "There are a lot of people out there whose minds aren't made up. They're up for grabs, and they're going to go to the side that does the best job of selling its point of view.