So, just how powerful is the Israel lobby in the US?

Out of America: Perhaps no more than a dozen out of more than 400 Representatives are pro-Palestinian

Intimidated? Obama at the American Israel Public Affairs Committee (AFP/Getty Images)

As public grovels go, this one was pretty spectacular. Former Senator Chuck Hagel, who may or may not become the next US Secretary of Defense, was back in his old haunts on Capitol Hill for his confirmation hearings, trying to explain a remark he made a few years back, that "the Jewish lobby intimidated Congress" and did some "dumb things".

Name a "dumb thing", he was asked by Lindsey Graham, his Republican colleague for six years until 2009 – though you wouldn't have guessed it from the venom of the exchanges on Thursday. Hagel couldn't. Graham persisted. "Name one person who's intimidated by the Israel lobby in the United States Senate." A taut silence, then Hagel limply responded, "I don't know."

Public hearings, especially confirmation hearings, are one of the great shows of Congress. Hagel's made especially good theatre, largely because the reek of treachery was in the air. Here was a Republican who had abandoned his party and colleagues like Graham and John McCain, his one-time friend and fellow Vietnam war hero, by turning against the Iraq war begun by a Republican president.

Worse still, Hagel had backed Barack Obama, not McCain, in the 2008 election, even accompanying the Democratic candidate on a high-profile campaign visit to Iraq and Israel. And now here he was, back on Capitol Hill as Obama's choice to lead the Pentagon, about to collect his 30 pieces of silver. If anything, McCain's own grilling of his former pal was even more poisonous.

In the end the public drama may make little difference. Hagel did pretty poorly, seeming to be taken aback by the hostility of the Republicans, even though the latter had made no secret of it beforehand. But performances at confirmation hearings rarely change minds – and even more rarely is a President's nominee to an important post actually rejected. The Democrats and their allies hold a 14-12 majority on the Armed Services Committee, and 55 of the 100 Senate seats. That should be enough. The only way Republicans can block Hagel is by using the filibuster to prevent a final vote on the floor.

But what lingered in the mind was not the set-to over Iraq, or the suggestions that Hagel was "soft" on Iran (he once had the temerity to suggest direct negotiations between Washington and Tehran) but his exchanges with Graham over the "Jewish lobby". It's always a mistake to use that expression, and not primarily because it sounds anti-Semitic. I did so in a sloppy opening paragraph a few years ago, and was rightly excoriated by American readers. "Jewish lobby" is wrong on two counts. First, the lobby includes many non-Jews, most notably Christian conservatives. Second, many American Jews do not support the group's hardline policies over Israel. The correct term, as Hagel quickly acknowledged last week, is "Israel lobby".

And that is precisely what it is: one of the most potent advocacy groups in Washington DC, and not only here. Few of its spokesmen were more forceful than Ed Koch, the colourful former mayor of New York who died on Friday. Koch, child of Jewish immigrants from Poland, was a passionate Israel supporter, and accused Obama of "turning his back on Israel" by naming Hagel to the Pentagon, which he called "a terrible appointment".

There are those who claim that the lobby's clout is vastly exaggerated, insisting that far from being a sinister body subverting US foreign policy in one of the world's most unstable regions, it is pushing at an open door. Even without a lobby, the thesis runs, Americans would be overwhelmingly supportive of Israel. Which may be true, but misses the point.

Power lies in the perception of power, and the Israel lobby, led by Aipac, the American Israel Public Affairs Committee, is perceived to have a heck of a lot of it. Fall foul of the Israel lobby, with its financial muscle and ability to put the word out, and, it is said, your political career may be doomed. That, presumably, was what Hagel was getting at when he spoke of people in Congress being "intimidated".

Exhibit A in this argument is Chuck Percy, the three-term Republican Senator from Illinois said to have been defeated in 1984 as a result of an Aipac-led campaign against him. Percy's offence, according to a committee official at the time, was to have shown "insensitivity and even hostility to our concerns". Also mentioned is George Bush Snr's failed 1992 re-election campaign, to which his short-lived block on loan guarantees to Israel while it continued to expand settlements may have contributed.

True or false? It's impossible to say. What matters is the perception. But one thing is incontestable. Congress is overwhelmingly supportive of Israel. Probably no more than a dozen of the 435 Representatives can remotely be described as "pro-Palestinian", while the mood in the Senate may be divined from a 2000 resolution expressing support for Israel, signed by 96 of its members (Hagel was one of the four who did not).

Not for nothing did Pat Buchanan once describe Congress as "Israeli-occupied territory" – so much so that an Israeli prime minister at odds with the White House can bypass the President, making his case directly to an Aipac conference or on Capitol Hill. Take Benjamin Netanyahu when he delivered an address to Congress in May 2011. I remember the assembled lawmakers jumping up and down like jack-in-the-boxes to give him 29 standing ovations. Whatever else, Bibi would never have received an acclamation like that in the Knesset.

If Chuck Hagel doesn't make it to the Pentagon, opposition to him from the Israel lobby won't have been the only reason, or even the main reason. But one thing you can be sure of. A good few more on Capitol Hill will have been "intimidated".