It's interesting; I recall reading the speech before and learning about it, but I never looked too deeply into how it was acquired. But I did remember reading somewhere that it was acquired by Israeli intelligence, and I remembered learning the story later on. It's always fascinating to me how often intelligence stories (given their obvious secrecy) are separated from the fruits of the intelligence. We learn about plots stopped or carried out, but not the "how", because of the fear of revealing methods or sources. But I digress.

The story is given pretty well in Spies Against Armageddon by Raviv and Melman. Israeli intelligence gained a copy of the speech thanks to Viktor Grayevsky, in a spur of lucky moments that they write are the typical coincidences "upon which espionage agencies capitalize". It's important to remember that coincidences in the intelligence world only matter if someone takes advantage of them, and many end up unnoticed until hindsight catches up. Mr. Grayevsky called what he managed "young and foolish" in the book, saying he would have been killed or imprisoned for decades had he been caught. Grayevsky was born Victor Spielman, but changed his name in Poland and became a journalist, and became a senior editor for the official Polish news agency. His parents and relatives largely moved to Israel covertly to flee the eastern bloc, but Grayevsky remained behind. His father fell ill in 1955, which was the first contact, so to speak. He traveled to Israel to visit his father, and he began speaking to a "diplomat" in the Israeli embassy in Warsaw, who he didn't know was actually Israeli intelligence. This is actually quite common in espionage; it allows the intelligence officers to estimate the value of a target and gives the target plausible deniability to say they thought they were having a friendly conversation with a diplomat or otherwise innocuous individual. Grayevsky's visit to Israel apparently changed him, and made him an ardent Zionist.

Grayevsky's history is important, because he gained a very unpopular opinion in the Soviet Union by becoming a Zionist, and was constantly at risk for that. Grayevsky came across this incredible coincidence by virtue of, believe it or not, an affair. He was having an affair with a married woman, and he was set to meet her for coffee. She was busy, so he hung around in the party's Central Committee headquarters, waiting for her, where everyone knew him. After all, he'd been there plenty, and was a journalist. He noticed a thick booklet, and saw the title, "The 20th Party Congress, the speech of Comrade Khrushchev". And it was marked Top Secret.

This, I presume, is what he called "young and foolish". He knew, and others knew, that rumors about this speech had flown worldwide, and that everyone wanted a copy. So he asked his girlfriend if he could borrow the copy to read it, and return it, so she could put it in a safe. She agreed, believe it or not. This journalist, this Zionist Polish Jew in the Soviet Union at a very anti-Zionist and anti-Semitic time, took this top-secret speech home with him, casually, and read the speech. It shocked him. So he did what he thought was best, and went back to the Israeli embassy. He met with Israeli officials instead of returning it to his girlfriend, not out of malice for Poland he said, but out of love for Israel. Apparently, Grayevsky said that the Israelis turned white, and then red, as they noticed what he had. And then they asked to borrow it, and returned it an hour and a half later. Every page was photographed, the booklet was returned (late, but without consequence) to the girlfriend, and the speech was gained. Not by any special subterfuge or James Bond tactics, but in the more common way; by luck and well-placed feelings. Grayevsky never asked for, or received, any award.

Why weren't other Western powers able to get ahold of it first? They didn't get as lucky. They offered bounties reportedly, and tried to coerce spies to get a copy, but none managed. Carelessness led to Israeli success, with a healthy dose of luck and a good bit of charm towards the right person at the right time.

Israel does not look great, when you get the full story. Of course, that's not what other intelligence agencies saw. They didn't see that Israel got its copy out of Poland via diplomatic mail that had sat around for three days, and was introduced to the Shin Bet head Amos Manor by his assistant as "some speech by Khrushchev for the Congress" that came out of Warsaw, when Manor asked for a routine update. Manor said he told his assistant, when he returned with the speech, "You're an idiot. You are now holding in your hand one of the most important secrets in the world". It was developed, circulated, and the authenticity questioned heavily. Israeli PM David Ben-Gurion said if it was authentic, there would be a liberal regime in Moscow in 30 years (not far-off for when the Soviet Union did fall, for the record!). Israeli intelligence's esteem in the eyes of the world rose greatly because of this. They didn't see the luck, they saw the speech and the intelligence victory it represented. Manor had it handed over to the CIA station chief in Tel Aviv, and two days later, it was on the desk of the CIA Chief, Allen Dulles. And here's where the esteem especially came from: Israel never shared the source, of course, and that meant other powers only knew that Israel had managed to get its hands on one of the most secret documents in the world at the time. When the Americans asked Manor how he got it, he said, "Jim, we have an agreement between us that we do not reveal sources of information, and the agreement applies to this case as well". Two weeks later, the Americans concluded the speech was authentic, and asked to publish it. And Ben-Gurion gave his consent, but asked that Israel not be named as the source. And then it was leaked, as you saw in Rise and Kill First, to news outlets and read all over. Suddenly, Israeli intelligence was seen as a gleaming outfit, and CIA-Shin Bet cooperation became enhanced and grew in the years that followed. Israel was emboldened, and the Mossad took advantage; it began to reach out to Arab officials in officially hostile countries, and finally, it became clear that Israeli intelligence (with the right amount of confidence and poise) could place assets in quite a lot more places than was typically assumed. While this didn't all come solely from the Khrushchev speech, it certainly was greatly helped by it.

So, how was the speech received? It was indeed a global story, and was read widely. It was broadcast over Radio Free Europe and Radio Liberty, and printed copies tied to balloons were flown into the Eastern bloc. The speech on its own was already quite a big deal in the Soviet leadership, given its implications and attacks on Stalin. The Communist party in the United States lost a huge amount of its membership almost immediately, tens of thousands of political prisoners in the Soviet bloc were set free, and there were even hopes that revolution would follow in Poland and Hungary, and Poland saw large protests and Hungary saw a revolution (put down violently) not long after. The Chinese condemned it, calling it revisionist.

In short, it had worldwide implications.

As for the embarrassment, it was selectively shared. It caused embarrassment and helped strip away the lingering "cult of Stalin", which was in part the goal of Khrushchev in giving the speech, hence its selective distribution. But the embarrassment of having it leaked was a whole other story. Khrushchev wanted it spread, for the political effect he judged would be favorable to him, but not leaked in full. It was often read in summaries and it was not reported in full. There are those who claim that Khrushchev even wanted it leaked in summary, as a sign he was breaking with Stalin; journalist John Rettie, for example, had a summary read to him that he said he believed worked for the KGB, and tried to file a story on it, but it didn't make it through censorship, he claims. He claimed that the story, which ran in March 1956 (before the leak to the New York Times of the full text) was likely what Khrushchev wanted, but it was never the leaked full text. When that came out, it was embarrassing; both from the counterintelligence perspective and because it laid out in full a text that was shared more slowly with the Eastern bloc than it was with the West through Rettie (if Rettie is correct in believing Khrushchev authorized the summary).