It’s hard to believe President Obama could be having problems with Jewish voters in New York City of all places, but this Siena College poll suggests he may even be losing Jewish support in one of the most liberal enclaves in the country.

The poll, which surveyed about 70 Jews and thus needs to be taken with a serious grain of salt, found that just 35 percent would vote to re-elect Obama in 2012, while 52 percent would vote for someone else. It follows other recent nationwide polls, which have also shown a dip in Obama’s Jewish support.

Unhappiness with Obama in the Siena survey didn’t seem to cross over to other Democratic politicians, however. Sixty percent of Jewish respondents said they would vote to re-elect Sen. Kirsten Gillibrand, while just 22 percent said they would support someone else.

It’s tempting to dismiss these numbers off-hand because the sample size was so miniscule, but there are other indicators Obama’s Israel policy could be hurting him with Jewish voters in New York. For example, take the recent campaign by former Democratic New York Mayor Ed Koch, who is calling on voters to elect a Republican to fill Rep. Anthony Weiner’s vacant seat, as a rebuke to Obama over his Israel policy.

“If Jewish New Yorkers and others who support Israel were to turn away from the Democratic Party in that congressional election and elect the Republican candidate to Congress in 2011, it might very well cause President Obama to change his hostile position on the state of Israel and to re-establish the special relationship presidents before him had supported,” Koch said last week.

Even New York Democrats who disagree with Koch’s plan concede Obama has turned off some Jewish voters with his positions on Israel.

“The perceptions aren’t great right now,” Assembly Speaker Shelly Silver told the New York Daily News today, referring to Jewish opinions on Obama in the state.

But Silver said that instead of supporting Republican politicians, Democrats should be putting forward more proudly pro-Israel candidates.

“What we need is more Democrats who will go to bat for Israel, notwithstanding what a president may think,” he told the Daily News. “In order to change the perceptions, it’s important to elect more staunch Democrats who are supporters of Israel.”

While neither the Siena poll nor the anecdotal evidence can be taken as solid proof Obama is losing significant Jewish support in New York, combined, these examples should be enough to make the president and his campaign nervous.