There are a few reasons why the United States was seemingly strangely opposed, but they are very interesting!

Charles D. Smith speculates in his book Palestine and the Arab-Israeli Conflict that it was because the United States felt they had been deceived by promises that the French and British had made to stay neutral in the Middle East, and also their belief that the operation was silly and would never work to resolve the West's problems with Nasser. He also argues that the West lost diplomatic standing as a result, and couldn't criticize the Russian crushing of the Hungarian rebellion happening at the same time.

Israeli historian Benny Morris notes one of the funnier things to happen out of it all:

Ironically, after the British accepted the cease-fire, U.S. Secretary of State John Foster Dulles, from his sickbed (he was dying of cancer), privately berated them for having stopped their operation midway. "Why didn't you go through with it and get Nasser down?" Dulles asked his visitor, [British] Foreign Secretary Lloyd.

Still, we can only wonder if that was the whole story. There appears to have been more to why the US was so pointedly not helping the British when a run on the sterling began as a result of the Suez Crisis, and that is explored in The Suez-Sinai Crisis 1956 by Moshe Shemesh. Chapter 18, by Robert D.Schulzinger, explores the way the crisis affected the United States. He explains that the US, following the Suez Crisis, began to see itself as the major outside power with influence in the Middle East, and this may indeed have been part of the actual goal. As he notes:

On 5 January, 1957 President Eisenhower addressed a joint session of Congress on American policy in the Middle East. He reported that events in the region had "abruptly reached a new and critical stage...Just recently there have been hostilities involving Western European nations that once exercised much influence in the area. Also the relatively large attack by Israel in October has intensified the basic differences between that nation and its Arab neighbors. All this instability has been heightened and, at times, manipulated by International Communism."

The Middle East, he asserted, ‘has always been coveted by Russia’. He therefore requested that Congress provide $200 million in military aid to the countries of the region in each of the next two years to counter ‘International Communism’.

Was this a likely goal? Perhaps. Alfred Atherton, in the next chapter's essay, writes:

[The United States] opposed military action, not to save Nasser, but because it was convinced that such action would unify the Arab world behind Nasser, and also because it would offer an opening to the Soviet Union...At the same time, the United States did summarily reject a Soviet offer of joint action and warned against Soviet intervention, thereby seeking to make clear the difference between American and Soviet intentions.

So it does appear that, at least in part, the fear was that any type of support for the British and French would not provide a significant geopolitical success (as Smith wrote) because force would not solve the problem, and it would indeed lead to Soviet influence increasing. It's clear the US wanted to increase its own influence in the area, and while there's no guarantee that the Eisenhower Doctrine that came after Suez was conceived of before, the fear of Soviet influence in the Middle East was well-established before the war. So the United States hedged its bets, hoping to keep the French and British on their side but not necessarily blindly support them, and gain popularity in the Arab world, which it subsequently lost very quickly according to Atherton anyways.

When we get to the question of why the Americans thought change would be impossible by force, we should probably take a look at Eisenhower and the Suez Crisis of 1956 by Cole Christian Kingseed. Kingseed writes that Eisenhower thought that not only was public support for the operation itself insufficient among the British and French, and Eisenhower justified this by looking at British media:

The Manchester Guardian considered the Anglo-French action "an act of folly without justification." The Times, normally a Conservative newspaper, expressed a feeling of "deep disgust" and was astonished that the prime minister had committed himself without the support of the Commonwealth and the United States. No possible reasons of speed or expediency could necessitate a situation in which the president of the United States had to hear about actions of his British ally from press reports.

And those are just a few examples. Besides the lack of popular support for this kind of action, the deception was perceived primarily because...well...the British did deceive the Americans. For example, while on October 30 the British Prime Minister sent Eisenhower a message saying:

Nevertheless we would not wish to support or even condone the action of Israel. We consider that, in view of the massive interests involved, the first thing to do is to take effective and decisive steps to halt the fighting.

This, of course, is rather laughable. It didn't seem believable to Eisenhower, and it definitely seemed like deception to him as well. After all, he had already expressed earlier that day his deep concern over the ultimatum the British issued, and so this seemed altogether to be a lot more confusing than anything else, and a lot more underhanded. And, as Eisenhower noted still earlier that day, there was great concern in the United States about violations of the Tripartite statement. The Tripartite statement, for reference, does not refer to the Tripartite Axis during WWII but rather to a statement made in 1950 by Britain, France, and the United States, which said:

The three Governments declare that assurances have been received from all the states in question, to which they permit arms to be supplied from their countries, that the purchasing state does not intend to undertake any act of aggression against any other state.

And to drive home the point of this being a laughable claim, that the British were looking to halt the fighting, it should be noted that they gave their 12 hour ultimatum that same day to Egypt, and that they initiated hostilities less than a day later.

So with the feeling of deception, the fear of Soviet influence, the feeling that the British, French, and Israelis would not succeed, the feeling that the public was not in support of the British actions, and the fear of economic backlash, it's understandable that the United States chose the path it did. And as for the economic backlash, one last book to look at, called The Economic Diplomacy of the Suez Crisis by Diane B. Kunz. There, Kunz points out the fear of a cutoff of Arab oil to the rest of the world, and the economic costs something like that would incur. And indeed, this is what Eisenhower saw happen in the crisis:

Hoover announced that oil supplies from the Middle East were now virtually cut off. Sunken ships completely blocked the canal, while Syrians had sabotaged three pumping stations for the Iraq Petroleum Company pipelines, rendering them useless. Only the tap line that ran from Saudi Arabian oil fields remained open. The president suggested preparing heavy tankers and oilers for immediate use, but regarding the British and French oil problem, he "felt that the purposes of peace and stability would be served by not being too quick in attempting to render extraordinary assistance."

By the way, as an aside, the Hoover mentioned is Herbert Clark Hoover, Jr., the son of the former president, and he was serving as Under Secretary of State. The reality of such a blockade, and anticipation of one coming, is one Eisenhower saw from a mile away, according to Kingseed's book. In fact, as Kingseed put it:

As a chief of state, Eisenhower was incredulous at Eden's apparent dismissal of the economic repercussions if the Arabs united against Britain. Would the Arab states cut off all petroleum shipments to Great Britain and France? The question of oil shipments to Western Europe had been a critical concern to Eisenhower for months. As early as July, he had raised this issue in the NSC, and the Office of Defense Mobilization had prepared several memoranda outlining anticipated oil needs, alternate sources of petroleum, and possible solutions if Western Europe found itself in dire economic straits.

Hopefully that helps explain the fears, reasons, and justifications the United States likely considered in siding against the UK, France, and Israel in the Suez Crisis!