The concern mentioned most often: Not only does Schwartz strongly support abortion rights, but before entering politics, she ran a Philadelphia women's health clinic where abortions were performed.
"A dream candidate for Republicans," one Democratic strategist warned. Others note that the GOP has held on to two suburban congressional seats in recent cycles by painting Democratic challengers Lois Murphy and Kathy Boockvar as too liberal.
Schwartz's strategists bet it will play out differently - that her potential to become the first woman elected governor of Pennsylvania, along with memories of what Democrats called the 2012 Republican "war on women," would galvanize a winning coalition. Corbett's standing with female voters has been weak in polls, and many recall his suggestion that women need only "close your eyes" if they did not wish to view a mandatory ultrasound before an abortion, as an ill-fated bill proposed.
Schwartz helped found the Elizabeth Blackwell Health Center, a now-closed women's clinic, in 1975 and ran it through the end of 1988. It provided prenatal care, a birthing center, and other health services.
In a gubernatorial campaign, to be sure, Schwartz, who has not yet made her candidacy official, plans to focus on the economy and jobs rather than social issues. She has a reputation as a moderate on fiscal matters.
Republican strategists say a Schwartz candidacy could help mobilize their partisans as well as right-of-center independents for Corbett, who has been saddled with low approval numbers in polls and would benefit from passion in the GOP base.
"A Philadelphia liberal woman who ran an abortion clinic is not going to play in some parts of the state, particularly out west," said Republican strategist Nachama Soloveichik of the Pittsburgh firm Cold Spark Media. "The ads almost write themselves. In many places, she could be portrayed as someone who is 'not one of us' and 'doesn't understand our culture.' "
That said, Schwartz would "be a tough opponent - she's going to have a lot of money and she's a smart politician," Soloveichik noted. "But she has baggage. If I were Corbett, I'd be rooting for Schwartz to win after a bloody Democrat primary."
More than a year out, that is looking like a possibility. State Treasurer Rob McCord, also from Montgomery County, has made it clear he, too, intends to seek the gubernatorial nomination, and plenty of other Democrats also are running or exploring.
Tension over questions of Schwartz's electability spilled into the open Friday when Politico reported a testy e-mail exchange between Rachel Magnuson, the congresswoman's chief of staff, and Mark Nevins, a Democratic consultant advising McCord.
In a March 12 e-mail, Magnuson took issue with unspecified "ugly" comments she said Nevins had made about Schwartz to other Democrats. She copied the message to aides at the party's congressional campaign committee, and suggested such talk would cost Nevins' firm business.
""[T]hat's one of the most bizarre e-mails I've ever gotten," Nevins shot back. He said he sincerely believed Schwartz was a weaker candidate because she could be portrayed as too liberal.
Magnuson declined to comment. Nevins said Friday in an interview, "I previously supported and like Congresswoman Schwartz, but just think Rob McCord would be a better candidate."
Still, some Democrats say larger issues are at stake. They say a Schwartz run could energize Democrats still buzzing from the historic election of Kathleen Kane as attorney general, the first woman ever to win that office in Pennsylvania.
"I believe that is significant - there is something about seeing it happen that is really powerful," said Stephanie Schriock, president of Emily's List, the national group that recruits and helps fund Democratic female candidates who support abortion rights.
For Emily's List, Schwartz, an established political figure with a strong record as a fund-raiser, represents a prime opportunity to pick up a governorship in big state.
But how crowded will the Democratic field be? A survey conducted March 9-12 by pollsters Jefrey Pollock and Joe Hickerson for Emily's List tested Schwartz in three possible 2014 Democratic primary scenarios: a three-way race against McCord and Tom Wolf, a businessman and former state revenue secretary; a nine-candidate contest that included former U.S. Rep. Joe Sestak, the party's 2010 Senate nominee; and an eight-candidate race without Sestak.
In the first, Schwartz led with 31 percent, to 12 percent for McCord and 7 percent for Wolf. She had an overwhelming advantage in the Philadelphia media market - her home turf - and led among minority voters, self-described liberals, and women in the poll.
When brief biographies highlighting positive attributes for each contender were read to respondents, the standings were Schwartz 58, McCord 14, and 8 percent for Wolf.
In the pollster's hypothetical nine-way primary, Schwartz led the field with 18 percent, followed by Sestak at 15 percent. None of the other candidates polled better than 5 percent.
Without Sestak in the field, Schwartz polled 21 percent, followed by McCord and former environmental secretary Kathleen McGinty with 7 each.
The poll, based on telephone interviews with 601 likely Democratic primary voters, had a margin of error of plus or minus 4 percentage points.
At Thursday night's dinner meeting of Pike County Democrats, Forrest, a technology consultant who represents the Republican-dominated county on the Democratic State Committee, allowed that Schwartz would probably lose the county if she were the nominee.
"Philadelphia is the whipping boy up here," Forrest said.
But she said the congresswoman could make a competitive race of it in a county with a high number of emigres from New York and New Jersey, which is right across the Delaware River from Pike County.
Forrest also said that if Sestak, a former Navy admiral, were to get in the race, he would probably be her first choice.
Jane Cole, a county Democratic committee member from Lackawaxen Township, said she did not know much about Schwartz and had not focused yet on the 2014 race - beyond her conviction that Corbett must go.
"It's too early," Cole said, "but I sure would like to see a woman. Wouldn't you?"
Contact Thomas Fitzgerald at 215-854-2718 or firstname.lastname@example.org. Read his blog, "The Big Tent," at www.philly.com/BigTent.