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“We’re not even counting Wisconsin as swing state but already as Obama’s,” said Suffolk University pollster David Paleologos. “The Wisconsin election was less about national politics and more about whether Wisconsin sets a precedent for people recalling a politician every time something upsets them, rather than about broader national issues.”

But others disagree.

“The Walker victory puts Wisconsin in play this fall,” said former American Conservative Union Chairman David A. Keene.

“The effort to recall Walker has led to the development of a massive and sophisticated campaign infrastructure in a state that the Democrats won narrowly in 2000 and 2004 and that could switch this fall, denying Obama crucially important electoral votes.”

It was the fear that the recall drive could backfire that has a number of national Democrats to question the wisdom of the campaign against Mr. Walker and a number of GOP incumbents in the state.

Mr. Keene sees no straight line between Tuesday’s election results and the vice presidential choice. “Walker would be very controversial and Christie is anathema to many conservatives,” he said. “Neither strike me as what Romney needs.”

If the name of the game in November is turnout, Mr. Walker offer pluses and minuses. He may boost turnout for tea party sympathizers and GOP voters hostile to unions or it may union members and sympathizers of Mr. Obama and the Democrats. Many predict Mr. Romney will prefer a lower-wattage partner on the ticket.

Romney won’t take Walker or Christie,” Portland, Oregon-based pollster Bob Moore said. “Both are too controversial. Probably former [Ohio GOP Sen.] Rob Portman — someone that won’t be a major target. Walker would really energize unions. It would be like throwing gas on a fire. Walker winning won’t affect Romney’s plans.”

Some see the Wisconsin vote as presaging the fulfillment of most the hopes and dreams of a new center-right coalition to address government spending woes.

“It will be easier to win meaningful fiscal reforms by putting restraints on government growth and by reducing government spending in order to balance the budget, since government spending usually is at the expense of our economic recovery and growth,” said Mr. Yue. “If Romney wants a running mate to rally tea party activists and the GOP’s grassroots in battleground states, Walker would be a very attractive candidate.”