Both Bush and Carter are said to have suffered politically from pressuring Israel and I do agree with you in that they would have lost anyway without the difference it made, however the lobby's influence is a lot greater than the figures you cite portray. First of all, the effect is not restricted to Jews. It's an Israel
lobby, not a Jewish
lobby and Christian Zionists
are, as you noted, in the mix. So the lobbying just can't just be measured by Jewish voters, the Israel lobby can have a greater influence by spending money for the candidates of their choice than by merely locking up the Jewish vote.
Secondly, with legislative districting smaller groups can have outsized power and as the Washington Post notes
, Bush "got crushed in a small group of heavily Jewish precincts in states such as New York, New Jersey, Ohio and Florida". I agree that this wasn't a kingmaker but it did have an impact. And as the Observer notes
, that a president believes this may be enough of a demonstration of the lobby on the presidential stage, writing, "Yes, the Jewish vote turned against Bush. He had won 27 percent of it in '88, only 15 percent in '92. And the turn may well have cost him New Jersey and Ohio, states he had won by big margins four years earlier (and lost narrowly to Clinton). But Clinton won the presidency in '92 by a resounding electoral margin, 370 to 168, and Bush's gaining N.J. and Ohio wouldn't have changed the outcome. Maybe there's a more extended analysis of how AIPAC and pro-Israel money changed the '92 race, but I haven't seen it... But let's focus on what matters here. A former President believes that the pro-Israel lobby cost him his job. His son runs for President and is far more responsive than his father was to the Israel lobby. Right there you have a good indication of the power of the lobby."
And there's plenty of evidence of the power of their lobby even in the current administration. Not just in his meetings with AIPAC while campaigning, his campaign stop in Israel, or his open letter calling for "unshakable" support for Israel (PDF file from AIPAC site)
but by events like him backpedaling on settlements, and even more clearly how Charles Freeman's criticism of Israel made him unacceptable for the intelligence post he was nominated for. The NY Times writes
, "The lobbying campaign against Mr. Freeman included telephone calls to the White House from prominent lawmakers, including Senator Charles E. Schumer, the New York Democrat. It appears to have been kicked off three weeks ago in a blog post by Steven J. Rosen, a former top official of the American Israel Public Affairs Committee, a pro-Israel lobbying group."
This lobby has undeniable influence in the executive branch, and this is even from an administration that is more willing than typical to push back against it
Lastly, The Israel lobby doesn't just attempt to sway Americans to vote pro-Israel (general presidential elections isn't their main battle ground) but mainly to get congress to and they make large political contributions that just aren't matched by any competing pro-Palestinian lobby. The largest of these lobbies, AIPAC, is a legendary Washington lobby. Fortune magazine ran a poll of members of Congress, staffers and aides to rank the most powerful lobbies in America
and AIPAC finished 2nd, ahead of the NRA and the Christian Coalition. All the last two administrations had both president and vice president attend their conferences and that they are Washington heavyweights is simply no secret.
The Israel lobby is changing, with newcomers like J Street
challenging the right-wing representation and there is talk of resentment in Congress of AIPAC these days but this is no slouch of a lobby by any stretch of the imagination, and taking them on directly will cost any politician significant political capital right now.