American voters now think President Carter's handling of the Iranian hostages situation has been "a failure." But they still are willing to back him on future steps he might take, and they still don't think the hostage policy should be debated in the campaign.

On the heels of the unsuccessful trip of the U.N. Commission of Inquiry to Iran, a 47-to-31 percent plurality of voters nationwide rate Carter's handling of the situation "a failure." Only five weeks ago, a 51-to-32 percent majority felt his approach to getting the hostages freed unharmed was "a success."

By the same token, when asked to rate the job he has done in "handling the Iranian situation," a 55-to-43 percent majority gives him a negative rating. In mid-December, a substantial 66-to-32 percent majority supported his handling of the crisis.

But the emotional commitment of the American people to getting the hostages back alive apparently runs so deep that they have not given up on supporting further steps the president might take:

By 72 to 23 percent, a big majority feels "personally deeply involved emotionally with the fate of the hostages," and is "willing to wait as long as necessary to get the hostages back unharmed.'"

By an even higher 76 to 17 percent a majority also agrees with the claim that "by being so patient for the past four months, President Carter has kept alive the chance that one day the hostages will be returned unharmed." h

And, of significance to the election campaign, a 60-to-37 percent majority still feels that "as long as the hostages are kept captive it is wrong for other candidates for president to criticize President Carter's policies on Iran."

These deeply felt sentiments of the public, based on the hope that the hostages can be returned alive and safe, keep Carter from losing public support on Iran altogether. However, how long public patience will continue to give the president the freedom to conduct slow and painful negotiations is in question. Clearly, erosion of the pre-Christmas unity already has set in, and events in Iran appear to be contributing toward a further decline.

A 77-to-16 percent majority of the voters nationwide now would like to see a change in U.S. policy about the hostages and would favor "tightening trade restrictions on Iran to force them to give up the hostages."

By the same token, a 51-to-39 percent majority is skeptical of the current tack of the administration to continue to work through the United Nations to negotiate the release of the 53 Americans now held in Tehran, feeling that "if we depend on the U.N. to get the hostages back, it may never happen, because the U.N. is such a weak and ineffective organization."

Public impatience is also evident in many ways with the way the hostage situation has evolved:

By a 71-to-24 percent, a substantial majority feels that "up to now, the United States has been at the mercy of the ayatollah, who has made us look weak and helpless."

By 53-to-34 percent, a majority rejects the president issuing an apology for past U.S. support of the shah as the price to get the hostages released unharmed. Most feel that "even if it was the only way to get the hostages back unharmed, it would be humiliating and wrong for President Carter to apologize for the U.S. role in supporting the shah."

If the time comes when the public is willing to see a full discussion of the hostage issue by candidates for president, one of the major sources of controversy will revolve around Carter's policy during the first 72 hours after the hostages were seized. By 60 to 31 percent, a majority is convinced "it was a big mistake not to give Iran an ultimatum in the first 72 hours after the hostages were seized in our embassy in Tehran."

The potential political impact of the Iranian situation is evident in dramatic terms in this latest ABC News Harris survey, taken among a cross-section of 1,002 likely voters nationwide.

Among the 31 percent of the voters who feel that the Carter policy up to now has been a success, Carter is preferred over Ronald Reagan by a 70-to-26 percent majority. Among the 47 percent who feel the Iran policy has been a failure, Reagan is preferred by 56 to 39 percent over Carter.

Even in the Democratic contest for the nomination, those who give the president a positive rating on Iran are inclined to vote 71 to 25 percent for Carter. Among those who give negative marks to his handling of the hostage situation, a 55-to-40 percent majority are inclined to vote against him.