If the Panama Canal treaty survives a Senate vote, it won't be because the anti-treaty forces didn't overwhelm friends of the Carter White House on the public relations front.

While Senate and House treaty opponents blitzed the country - spending about $80,000 for one whirlwind, airborne publicity tour last month - the pro-treaty forces only weeks ago got around to making a direct mail appeal for support from voters. This, is spite of the fact that since last fall mail against treaty ratification ran as high as 1,000-to-1 in some senatorial offices.

Heading the Carter lobbying effort are S. Lee Kling, former treasurer of the Democratic National Committee, and Jack Marsh, a White House counselor to Gerald Ford. Their committee of Americans for the Canal Treaties budget was, as of January, only about $200,000, and they have opted for speeches and local efforts instead of a massive direct effort.

Among those treaty supporters who disagreed with that plan were Tom Mathews, who is to liberals what Richard Viguerie is to conservatives: a direct mail expert with lists of sympathetic supporters. In conjunction with former Delaware governor Russ Peterson - who until recently headed a kind of international Common Cause called New Directions - Mathews last month mailed 1.1 million appeals to people who subscribe to magazines such as the Washington Monthly and the Nation. The request: write your legislator to counter the tide of anti-treaty letters. More than twenty liberal groups raised the funds and provided others other names for the mass mailing.

"Some people tended to think of this in terms of a presidential campaign instead of in terms of citizen action and citizen concern," grips Mathews. Others have harsher words for the White House effort, begun early last fall at the direction of Hamilton Jordan.

"You've got to have proven lists and when you have monetary and time constraints . . . our finances are relatively limited," admits Marsh, who joined the fray at the suggestion of Gerald Ford. Marsh, for one, thinks that if his side had raised more funds, passage would not be the close test observes expect: "Our experience is the more people know about the treaty, the more favorable they're likely to be about it."