What happens to the rising political fortunes of President Carter after Iran? There are at least two competing theories as the crisis continues to dominate the news, pushing the presidential campaign into the background.

One was voiced to reporters last week by Republican John B. Connally, who could have been speaking for the presidential challengers of both major parties.

Connally said the president's surge in public opinion polls since the Nov. 4 takeover of the U.S. Embassy in Tehran is "an aberration." Carter, he said, is enjoying "a second honeymoon" based largely on the patriotism of the American people who traditionally rally around a president in a time of crisis.

But after Iran, the former Texas governor predicted, "the specter of inflation, tight money and lack of leadership" will be pushed to the forefront and Carter's stature with the voters "may fall as fast as it rose."

White House and Carter campaign committee officials concede that some of what Connally says is true. "There is no question that part of it is a rallying around the president by the country," said Carter's pollster, Patrick Caddell.

But Caddell and other Carter partisans, offering a competing theory, differ with Connally's analysis in two important respects.

Caddell argues that the president's handling of the Iranian crisis has served as an "accelerator" of trends in public perceptions that were already under way. Even before the embassy takeover, Carter's standing was on the rise while that of his chief Democratic rival, Sen. Edward M. Kennedy (D-Mass.) was falling as his campaign got off to a shaky start, he said.

Moreover, Caddell says, the crisis has lasted so long, and has so dominated public attention, that it is likely to have a permanent impact on how the public views Carter as a leader.

The evidence of Carter's surge was dramatically illustrated in the latest Gallulp poll, completed Dec. 9. It showed the president not only leading the Republican presidential frontrunner, Ronald Reagan, in a head-to-head contest, but also gave him a 48-to-40 percent lead over Kennedy as the choice of Democratic voters. Two months earlier, before Iran and before Kennedy had begun to campaign, the Massachusetts senator led the president among Democrats by 60 to 30 percent.

George Gallup described this turnabout as "stunning," and called the overall jump in public approval of Carter's performance in office "the largest increase in presidential popularity recorded in the four decades the Gallup poll and Gallup organization have made these measurements."

But the key question for Carter's reelection chances is whether the gains of the last two months can be sustained. And on that question, the fickleness of public opinion as measured by polls and Carter's own record of rising and falling public esteem are far less comforting to the White House than the latest Gallup figures.

In September 1978, the president achieved a dramatic foreign policy breakthrough with the signing of the Camp David accords for an Egyptian-Israeli peace. In the next Gallup polls, Carter's approval rating surged 17 points, from 39 percent to 56 percent. Gallup reported that this was "the sharpest gain for a chief executive in four decades of Gallup poll presidential popularity measurements," a record that stood until Carter broke it again during the ongoing Iranian crisis.

Gallup has written, "Past history indicates a president's rating dramatically climbs after a particular event, but ebbs to the level recorded prior to the event in about six months."

By the end of last March, just after the signing of the Egyptian-Israeli peace treaty on the White House lawn, Carter's approval rating was back to 39 percent. Later this year, it sank even lower, until the recent surge.

In a post-Iranian crisis atmosphere, a similar plunge in public approval could have a devastating effect as the president heads into some of the large-state primaries in March and April. There is no question that his challengers will try to accelerate any downward trend by refocusing public attention on inflation, a possible recession, high interest rates and energy problems.

White House and Carter campaign aides say they expect a post crisis decline and concede that they cannot much longer count on a series of Kennedy mistakes to help their cause.

The White House, starting from the Caddell thesis that there will be a lasting change in public attitude toward Carter's leadership, hopes to stem any decline by building on its new foundation of public confidence.

With the crisis in Iran continuing and its outcome very uncertain, presidential aides are reluctant to talk about this.

With the country angry over the Iran crisis, the president is also displaying a much more hawkish attitude on military issues, a far cry from his 1976 theme of cutting defense spending. Kennedy appears to be moving to the right on this and other matters -- as evidenced by his refusal to criticize the huge defense spending increase the president proposed last week -- but Carter is moving just as fast, courting a public that White House aides believe has been cleansed of its "Vietnam complex" by Iran.

However, neither these nor other measures will immediately affect the nation's underlying economic troubles, which Kennedy and the others are counting on to drag Carter down once again.

Carter campaign chairman Robert S. Strauss is a master of the political game of deliberately setting low expectations that can be exceeded, but last week, as White House aides spoke of the Iranian crisis "blunting" the so-called leadership issue and with the president surging in the polls, he spoke with conviction when he said, "It's going to be an exceeding long, hard campaign."