(CNN) - A second straight poll of New York State voters indicates that Sen. Kirsten Gillibrand of New York holds a double digit lead over a potential Democratic challenger.
But the Siena Research Institute survey, released Monday, also indicates that more New Yorkers have an unfavorable view of Gillibrand than have a favorable view.
Former Rep. Harold Ford Jr. of Tennessee last week announced he's considering a primary challenge to Gillibrand, a former congresswoman from upstate New York who was was named a year ago to replace Sen. Hillary Clinton, who stepped down from her Senate seat after being confirmed as secretary of state.
Gillibrand is running this year to serve the final two years of Clinton's term. Ford, a former five-term congressman who narrowly lost a 2006 bid for the Senate in Tennessee, now lives in New York.
According the the Siena poll, Gillibrand leads Ford 41 to 17 percent in a hypothetical Democratic party primary match up, with 37 percent undecided. Gillibrand had a 19 point advantage over Ford in a Marist College survey released Friday, with one in three voters undecided.
But some other results in the poll also spells trouble for Gillibrand.
"After one year as senator, for the first time ever, more voters (32 percent) view Gillibrand unfavorably than those (30 percent) who view her favorably," says Siena pollster Steven Greenberg.
The survey also indicates that 29 percent want to elect Gillibrand, with 45 percent saying they'd perfer someone else.
Ford's move may anger the White House, which supports Gillibrand and has helped clear the field of any potential Democratic rivals. According to the Marist poll, Democrats are split over whether President Barack Obama's backing would make them vote for a particular candidate.
Republicans are without a big name candidate at this time. Former New York City Mayor and 2008 GOP presidential candidate Rudy Giuliani has said no to a senate run, as has nine-term Rep. Peter King. Former New York State Gov. George Pataki has not indicated that he wants to make a bid. According to the Siena poll, Pataki tops Gillibrand 51 to 38 percent in a hypothetical general election matchup, with the former New York governor beating Ford by an even larger 54 to 32 percent margin.
The Siena was conducted January 10-14, with 806 registered New York State voters questioned by telephone. The survey's overall sampling error is plus or minus 3.5 percentage points.
Follow Paul Steinhauser on Twitter: @psteinhausercnn