Just how far the party has traveled toward relevance will be tested May 20, when Wolfe, a lawyer in University City, runs for City Council in a special election. An at-large vacancy was created when Bill Green left Council to chair the School Reform Commission.
Wolfe's opponent, State Rep. Ed Neilson, could not be more representative of the need to finally crack the Democratic stranglehold on power, Wolfe said.
After statewide redistricting, Neilson would have been forced to square off against fellow Democratic State Rep. John Sabatina Jr. Instead, the city's Democratic ward leaders hand-picked Neilson for the Council race to avoid a nasty primary. (Wolfe, a GOP ward leader, was picked by his party leaders, as well, per the special-election rules.)
"What was the analysis in selecting my opponent? Was it, 'What's best for Philadelphia?' " Wolfe said. "No, it was, 'What's the most expensive race we're going to face? How can we preserve our resources to sustain ourselves?' "
Born in Pittsburgh and raised in Elkins Park (his parents hailed from West Virginia; his father worked for television maker Philco), Wolfe, 58, is a peculiar species of urban Republican.
He has lived in West Philadelphia since his undergraduate days at the University of Pennsylvania, where he first got involved in Republican politics, and he espouses a love of city living and public transportation that probably would roll the eyes of many state Republicans.
He stands on solid GOP ground when he talks about reforming the city's public employee pension system and work rules, but those are also positions to which Mayor Nutter, a Democrat, has been holding fast for most of his two terms.
Wolfe hews close to party orthodoxy on taxes (raising them is "one of the worst things you can do") and school choice (he supports expanding charter schools.)
But he refuses to situate himself on the political spectrum.
"This is a city election. We have to fix potholes," he said. "I'm out there talking about city priorities."
He and the party hope to attract independent and Republican voters in May, in part by pushing opposition to a ballot question.
That question will ask city voters whether they want to end the requirement that elected Philadelphia officials must resign if they want to run for another office.
Wolfe likens ending the rule to paying politicians to look for new jobs - a "Not on our Dime" Twitter handle and Facebook page were started last week by the new GOP executive director, Joseph J. DeFelice.
But in a city where registered Republicans are outnumbered 61/2-1, trying to motivate the base with the resign-to-run issue could create another schism in the party. The drive to end the rule was led by at-large Councilman David Oh, one of three Republicans now holding elective citywide offices.
"That does kind of make things a little awkward," Oh said last week after his own party voted to oppose his ballot measure. "But, look, people don't have to agree with me."
Oh said the rule encourages a political stagnation that plays into the city's one-party rule - Democrats typically can hold office as long as they like, so they rarely risk leaving safe jobs without party approval and backing.
(Nutter was an exception, resigning from Council to pursue an underdog campaign for mayor in 2007.)
DeFelice said Republicans must reach into new areas of the city, be open and transparent, and generate some buzz.
He launched the party's first social-media sites, and he has been using them to poke fun at Democrats, such as the state House members alleged to have taken cash from an undercover informant in an ill-starred sting investigation. He recently built a March Madness-like bracket with the "Underhanded Eight" worst ethics violators.
"It could have been a little juvenile," he said, "but it got us good play."
DeFelice said the party was likely to run fewer but better-qualified candidates in coming years.
"We need to start appealing to voters and letting them know the Democratic Party isn't necessarily the best for the middle class," he said.
Wolfe agreed, calling the Democratic Party an "oligarchy."
"They don't care about you," he said. "They care about getting reelected, pandering to special interests, and amassing political power."
Democrats have ruled more or less without opposition since Mayor Joseph S. Clark Jr. was elected in 1951. The last Republican to defeat a Democrat in a citywide race was Ronald D. Castille running for district attorney in 1989.
"This is going to take time," DeFelice said. "I'm not naive."
Despite the long odds, Wolfe said he was "in this to win . . . I'm not just going through the motions."
"I'm hopeful that if I don't win it, then some positive will come out of it," he said. "That maybe people will look at some issues in a different way."