Last week Specter, 79, abandoned the Republican Party to run for re-election as a Democrat, a move denounced by fellow Republicans but welcomed by the country's top Democrat, President Barack Obama.
Specter said his philosophy was more in line now with Democrats than Republicans, who fired back that he was simply bending to the political winds in order to hang on to power.
A Quinnipiac University poll found Specter would defeat a conservative Republican who is in the race, Pat Toomey, if the election were held today by 53 percent to 33 percent.
But the picture was much closer if a popular former governor of Pennsylvania, Republican Tom Ridge, were to jump into the race.
The poll found Specter leading Ridge by only a margin of 46 percent to 43 percent.
Before Specter's switch, Toomey had a large lead in polls looking at the potential Republican primary vote. Monday's Quinnipiac poll said Republicans still back Toomey 74 percent to 18 percent over Specter.
"A former Republican senator running as a Democrat against a popular former Republican governor seeking to make a political comeback would be a battle royal in Pennsylvania," said Clay Richards, the assistant director of the poll.
Specter can be expected to be supported in his race by Obama, who carried Pennsylvania decisively in defeating Republican presidential candidate John McCain last November.