ST. PAUL — It wasn’t so long ago that Minnesota seemed like an attractive target for an emboldened GOP trying to expand its list of presidential battlegrounds. But a financial tailspin at state party headquarters and allegations of infidelity involving one of the party’s young stars have Republicans watching in horror as their brand is tarnished.

The worst-case scenario for Republicans: that donors will see the party as a bad investment, diverting resources that might have been spent making the Obama campaign defend once-friendly turf; and that grass-roots activists, turned off by scandal and dysfunction, will sit out the election cycle.

While a Republican presidential campaign “will invest in Minnesota if it thinks they can win it, they will also look at how well the party is doing its basic functions — identifying Republicans, getting out the vote,” Scott Cottington, a St. Paul-based political consultant who works on GOP campaigns around the country, said Tuesday. “They will make a decision based in part on the strength of the collective effort.”

The potential problems reach far deeper than presidential politics. Newly won Republican majorities in the state House and Senate started to look wobbly last week when Senate Majority Leader Amy Koch abruptly resigned her leadership post and said she wouldn’t seek re-election. A day later, several of her Republican colleagues said Koch quit only after they confronted her with rumors of her “inappropriate relationship” with a Senate employee.

But that was only the worst piece of news on a terrible day for Republicans. The same day Koch’s colleagues went public with their claims, the front-runner to take control of the financially troubled state party dropped out of the race after revelations of an arrest for expired car registration and an earlier sexual harassment lawsuit. And a Republican candidate to challenge popular Democratic Sen. Amy Klobuchar next year admitted a 2005 arrest for carrying a loaded gun at the Minneapolis-St. Paul International Airport.