Hillary Can't Hold NYC

Hillary Clinton might have expected a boost from her bold declaration that she is running for the Senate, but the numbers are showing just the opposite, reports CBS News Correspondent Diana Olick.

The latest Marist College poll released Wednesday shows the First LadyÂ's numbers are dropping in a dangerous area for a Democrat: New York City, a key Democratic stronghold and the center of the state's Jewish community.

This comes just a day after Clinton took her swipes at Mayor Rudolph Giuliani during a meeting with black clergy in Manhattan.

"Criminalizing the homeless with mass arrests for those whose only offense is that they have no home is wrong," she said. "Locking people up for a day will not take a single homeless person off the street. It will not make a mentally ill person who should be in an institution any better."

Giuliani defended his homeless policies, which include denying people the use of shelters if they refuse work assignments, and charging those found sleeping in public places with disorderly conduct or other minor crimes if they refuse to move along.

Taking a dig at the fact that Clinton has never lived here, he added: "People who are not familiar with (New York) can miss the reality of what's happening. To take some of the few situations when people are arrested is to misunderstand the program."

A new poll issued Wednesday made the Clinton-Giuliani race a statistical dead heat, with the mayor getting 46 percent and Clinton 43 percent of the support of 800 voters questioned statewide. The Journal News-Manhattanville College poll found weaknesses for Clinton in the downstate suburbs, where Giuliani led 59 percent to 34 percent, and among women, where the candidates were about even.

The poll, taken Nov. 18-23, has a margin of error of four percentage points for the statewide sample and seven percentage points for the smaller suburban sample.

Giuliani, a Republican, spoke to reporters in Houston, where he was raising money for his own likely Senate campaign.

"We do more for homelessness than the city has ever done before," said Giuliani. "The response to homelessness is not some romanticized, general response."

He said drug-addicted and alcoholic homeless people are put in treatment, "but there is a certain number of homeless people not all, not the majority who are criminals or who are wanted for crimes. The only people who get arrested are wanted for crimes, or have committed a crime."

He added: "The basic response used to be to ignore people who were living on the streets. Now we are dealing with it, dealing with the consequences of mental illness."

Giuliani instituted the arrest policy after a woman was critically injured by a man believed to be homeless, who hit her on the head with a brick.