By Tuesday, politicians will have left this state, and if the polls and the professionals are correct, President Carter will have renewed his claim to the presidency and the invincibility of GOP front-runner Ronald Reagan will have been put to question.

The Iowa precinct caucuses Monday night will be the first test of the 1980 presidential campaign. Less than 10 percent of the state's 1.6 million registered voters are expected to take part. But their decisions will help set the tone of the campaign for the rest of the year.

The Democratic race has the most symbolism and has understandably attracted the most attention. It was in Iowa last March that disgruntled labor leaders formed the nation's first draft-Kennedy group and the pressure for Kennedy to challenge the incumbent president began. And it was the 1976 Iowa caucuses that gave Carter his first boost on the way to the White House.

Carter is riding a wave of popularity here and if this were a primary election he would be expected to win handily. But caucus elections are won or lost on the ability of a candidate to get his supporters out. And the Kennedy organization, interviews around the state indicate, is as good if not better than the Carter one.

Ironically, results may hinge on how many caucus-goers are dissatisfied with both men and choose to support uncommitted slates -- something California Gov. Edmund G. (Jerry) Brown Jr. urged his backers to do this week. Party leaders estimate as many as one-third of caucus-goers may be uncommitted -- an estimate that has grown steadily in recent weeks.

Republican results may be more interesting. For months Reagan, a Des Moines sportscaster before he went to Hollywood to become a screen star, has held a comfortable lead over his five major opponents here but has made only perfunctory campaign appearances in the state, and his advisers concede that Reagan's refusal to participate in a debate with GOP opponents here damaged him.

Supporters of George Bush, who a few months ago was just an asterisk in polls here, are hungry for an upset, or at least a strong second-place finish. The battle for third appears between John B. Connally, the former Texas governor, and Sen. Howard H. Baker (R.-Tenn.) with Sen. Bob Dole (R.-Kan.), Rep. Philip Crane, (R.-Ill.) and Rep. John Anderson, (R.-Ill.) competing the field.

Bush adopted the same strategy Carter used here four years ago. He has spend more time in Iowa than any other candidate -- 27 days in the last year -- and has built up a more elaborate campaign organization than his rivals. The organization has identified Bush supporters in every precinct in the state. This week each was mailed a caucus kit telling them where to go and what to do Monday night. Before the weekend is out, each is supposed to receive two phone calls reminding them to vote.

Baker and Conally, who got a later start building up campaign organizations, have relied heavily on advertising and a massive 11th-hour telephone blitz.

Reagan has depended largely on his long standing popularity here. The few advertisements he has had on the radio do little more than urge supporters to attend the caucuses. Many of these supporters are not traditional Republican Party members and Reagan's biggest worry is they may not be as inclined to go to the caucuses as will be Bush backers, who Reagan aides describe as "charity ball types who love to go to committee meetings."

Reagan, making three final stops in the state today, said he remains "very cautiously optimistic" about the caucuses.

Privately, some Reagan supporters today said they feared a Bush victory. Lt. Gov. Terry Branstad, a staunch Reagan supporter, said he thought Reagan "had turned it around in the last three weeks" and would win Monday. But he was openly critical of the way the campaign has been conducted.

"There was a feeling he was neglecting Iowa," said Branstad, who urged Reagan to participate in the Iowa Republican debate. "John Sears [the campaign manager] won't admit it but I think they ran a poor campaign in this state."

Bush, making a campaign swing through the state Friday and today, tried to downplay talk about a possible upset. "I've been trying to lower my Iowa expectations," he said. "There is a tremendous optimism, but I'm not going to be unrealistic."

But Bush backers in many places were talking confidently. "Six months ago Bush was hardly known. A lot of people were for Reagan. But that's died down," Roy Pogge, a Council Bluffs attorney said at a rally. "Bush has gradually been going up. I predict he'll beat Reagan or he'll at least be second."

Rep. James Leach (R-Iowa), who is traveling with Bush agreed: "I think he'll win in my district. My organization is his organization . . . the country is yearning for a new Republican."

Connally, nearing the end of his 40-hour marathon through the state, continued to predict a Bush victory over Reagan, but could not be coaxed into predicting a third place finish for himself ahead of Baker.

This Middle American state may seem like a strange, unrepresentative place to start the 1980 campaign. In many ways, it looks like the America that used to be -- largely rural, almost all white (99.4 percent) and patriotic. Its government is progressive, its sky is clean.

Polling done by the Des Moines Register offers some fascinating insights into the people who live here. The newspaper found 59 percent of the people of the state say they are in love with Iowa. Forty-nine percent say they are for the Equal Rights Amendment. Fourteen percent own CB radios. Seventy-five percent favor spanking in schools. Forty-seven percent say blue is their favorite color. And 52 percent claim they tell someone, "I love you," every day. Only 5 percent of Iowans think they will end up in hell, but 30 percent are cynical enough to believe their neighbors might.

But the state has been somewhat of a political bellwether in the past. Dwight D. Eisenhower beat Robert Taft in the 1952 GOP caucuses here. In 1968 Iowans used the caucus to criticize the U.S. involvement in the Vietnam War. In 1972, Sen. George McGovern made a surprisingly strong showing here before going on to become the Democratic Party nominee. And then there was Jimmy Carter in 1976.