Former Alaska governor Sarah Palin (R) teed off on Treasury Secretary Timothy F. Geithner on Thursday night, saying she does not believe his “false statements” that a “catastrophe would befall” the country if Congress fails to raise the debt ceiling by August.

On her first day in New Hampshire, Palin held an impromptu news conference as she was leaving a clambake here. She encouraged congressional Republicans to hold firm in the debt-ceiling negotiations, and she said the cost of the war in Afghanistan and the posture of the Afghan government should prompt consideration of a quicker drawdown of U.S. forces there.

Geithner, she said, has “given us now four different due dates where catastrophe would befall us if the debt ceiling is not raised. . . . Well, once bitten, twice shy. How many more times are we going to have to hear this date change?” Of the August deadline Geithner says is the absolute cutoff for congressional action, she said, “I don’t believe it.” She urged Republican leaders in Congress not to give in to the Obama administration’s demands, saying it would be “a failure of leadership” to yield at this point.

Palin arrived in New Hampshire on a week-long bus tour up the East Coast even as former Massachusetts governor Mitt Romney was wrapping up his formal announcement of candidacy for the GOP nomination in nearby Stratham.

After mingling for more than an hour with invited guests at the clambake, she responded to a series of questions from reporters who had gathered to watch.

Her comments on Afghanistan added to growing doubts about an extended stay for U.S. forces. Palin said it is time to reevaluate the U.S. mission there.

“We need to know in Afghanistan, especially now that [President Hamid] Karzai is pulling his stunt there and telling NATO that perhaps we’re not as welcome as we thought we were,” Palin said, adding, “If the host country doesn’t want us there, then we have to reevaluate our involvement there. With Afghanistan, with Iraq, too, and now with Libya, the cost of the war has got to be considered.”

She was also asked about whether her bus trip might yet lead to a presidential candidacy and specifically what kind of reception she was getting in the state with the nation’s first primary.

“There’s nice encouragement around here,” she said. “I think there’s just around the nation a strong desire for true change in America to get the economy on track, and that certainly was illustrated here.”

About three dozen people, along with a clutch of journalists, greeted Palin when she arrived for the clambake. Among them was former New Hampshire governor John Sununu, who earlier had attended Romney’s announcement.

The menu was steamers and corn on the cob, but Palin also brought six lobsters with her to add to the feast.

The crowd included only a few other notable political leaders: veteran strategist Mike Dennehy; Shannon McGinley of Crossroads, a New Hampshire social conservative organization; and a former GOP candidate for Congress, Jennifer Horn.

As the weather turned colder and the wind increased, Palin put on a blue sweatshirt with “New Hampshire” emblazoned on the front. For more than an hour, accompanied by her daughter Piper, she chatted animatedly with the others. One woman asked for her autograph and said, “You have to make an announcement this week — you have to!”

Palin replied with a laugh, “Oh, do I! You’re the strategist.”