The leader of GOP House election efforts is newly confident in the wake of yesterday’s victories in special elections in New York and Nevada, declaring that Republicans will go on offense in more places now – and that the party has found a way to overcome Democratic attacks on Medicare.

“The race was about the Democrats’ agenda, the president’s popularity, and his policies,” said Rep. Pete Sessions, the chairman of the National Republican Congressional Committee. “It was his policies that came into focus and scrutiny and play. And that’s why we won both these races, and we won ‘em big.”

Reminded that – after a special-election defeat – Sessions had said in May that such races are “poor indicators of broader trends or future general election outcomes,” he added a caveat.

“That’s correct — unless the president of the United States is involved and you put your entire playbook behind these two races that have gone on,” he said. “They came after us on Medicare. They came after us on the president’s agenda. When you have the fourth-largest Jewish district, at NY-9 … That is a national implication.”

The race means Republicans can expand the playing field in 2012 House races, said Sessions, R-Texas.

“When you can take a district that has not elected Republicans since the 1920s, it means that we can get great candidates — better candidates I think than what the Democrats have as sitting members of Congress — and be competitive. And we will certainly be on offense, as the NRCC has always been under my tenure. We will be on offense to go pick up seats all across this country.”

Among the lessons of the races, Sessions said, is that Republicans can fight back successfully at Democrats who try to portray them as seeking to dismantle Medicare.

“We’ve turned the corner on the Medicare message. We feel very good about that,” he said.

As for the president”s congressional agenda, Sessions declared that the Obama jobs bill is going nowhere in the GOP-controlled House.

“People recognize that’s $447 billion worth of more federal government spending, and $447 billion worth of taxes that comes from the job creator directly to the government. That’s an inefficient transfer. It’s dead on my arrival,” he said.

And Sessions, who’s endorsed his home-state governor, Rick Perry, for president, said he’s glad to defend Perry’s record against rivals who are questioning his conservative credentials.

“Rick Perry is a conservative, but here’s what Rick Perry has really done: He has a model of success. That model of success: be pro-business, work with business leaders in job creation, make education competitive, make education really great. We have lots of good schools in Texas.”