But Toomey jumped out to a 14- point lead when the poll targeted "likely voters," people who said they are certain to vote and are paying close attention to the race.
Among that group, Toomey led Specter 45-31 percent, with 20 percent undecided.
"I can't deny it's all very encouraging," Toomey said. "But I'm also very aware of the fact that the election is nine months away. A lot can happen. So I'm going to run like I'm 20 points behind."
Specter, who narrowly beat Toomey in the 2004 Republican primary, declined to comment on the poll yesterday.
Toomey, who lives near Allentown, left his congressional seat for the 2004 race.
U.S. Rep. Joe Sestak, who is leaving his Delaware County congressional seat to challenge Specter in the primary, also came up a loser against Toomey in the poll. Toomey led Sestak among registered voters by 28-16 percent with 51 percent undecided.
With likely voters, Toomey's lead on Sestak grew to 41-19 percent with 37 percent undecided.
Sestak was unavailable for comment yesterday, a campaign spokesman said.
The poll found health care, the economy and jobs to be the top issues in the race.
The winner of the May 18 Democratic primary will have to deal with what Madonna calls the "enthusiasm gap."
Madonna notes that 47 percent of the registered Republicans in the poll said that they were likely to vote in the Nov. 2 general election, while only 35 percent of the Democrats felt the same way. He attributes that to national news of Democrats' struggling to implement their policies in Washington despite control of the White House and Congress.
Madonna pointed to Republican wins in races for governor in New Jersey and Virginia last year and in a U.S. Senate race in Massachusetts this month as proof that the GOP is energized and that many Democrats are staying home.
In Pennsylvania's race for governor, Madonna found the candidates so unrecognizable to voters that their current standing in the poll means little.
Seven in 10 people in the poll had no opinion on that race.
"They have no state name recognition," Madonna said of the candidates. "The fact is, the race is in a very inchoate form, a form that has yet to take shape."
The poll showed state Attorney General Tom Corbett leading state Rep. Sam Rohrer 23-5 percent in the Republican gubernatorial primary, with 69 percent undecided.
Allegheny County Executive Dan Onorato led the Democrats with 10 percent while state Auditor General Jack Wagner, Scranton Mayor Chris Doherty and Montgomery County Commissioner Joe Hoeffel each had 4 percent; 72 percent said that they were undecided.
The poll of 1,165 people, conducted from Jan. 18-24, has a margin of error of +/- 2.9 percent.