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“He’ll continue to speak clearly about what his priorities are,” Mr. Carney said. “He will make clear that, for example, we’re disappointed at the choices made by Republicans to allow the so-called sequester to take effect, with all of the negative consequences that result, but he also believes we can move forward and try to adjust these other challenges.”

That line of attack played out Sunday, with Rep. Debbie Wasserman Schultz, chairwoman of the Democratic National Committee, accusing Republicans, including Sen. Ron Johnson, of openly pulling for the economy to fail, for which Mr. Obama would presumably take the blame.

“Our friends [on] the other side of the aisle, unfortunately, like the senator, continue to root for our economy to not be going in the right direction,” the Florida Democrat said on ABC’s “This Week.”

“Absolutely not,” Mr. Johnson, seated immediately adjacent to Ms. Wasserman Schultz, shot back.

Treacherous ground for some

The “carrot” portion of the president’s strategy presents potent political risks — especially for moderate House Republicans, who are more likely than their colleagues on the right to vote with Mr. Obama on a given issue but are also some of the prime targets for defeat by Democrats in their push to take over the chamber next year.

Of the 33 House Republicans ranked as “potentially vulnerable” by political analyst Larry Sabato, 14 are considered moderate or centrist in their voting records. Only four of the lawmakers on the list are members of the tea party, which the administration singles out for most of its criticisms.

Rep. Charles W. Dent, a fifth-term lawmaker from Pennsylvania who voted with the administration on the “fiscal cliff” deal and on disaster aid for victims of Superstorm Sandy, said Mr. Obama can’t afford to alienate moderates if he is sincere about seeking compromise.

“Many of the people who are going to be targeted by the president and the House Democratic campaign committee are going to be members in marginal districts, people who in most cases are more apt to find common ground and seek compromise,” Mr. Dent said.

“We’re going to have to determine if the president is more intent on getting a big political victory in the midterm, or actually trying to collaborate and seek agreements on major legislative issues between now and 2014. That question hasn’t yet been answered.”

He said Republicans likely would be receptive to some of the president’s initiatives, such as Mr. Obama’s proposal in the State of the Union address to form a trans-Atlantic trade and investment partnership with Europe.

“I think the president has to make a choice: Does he really want to govern over these next two years, or does he want to wage a perpetual campaign?” Mr. Dent said. “If he wants to cement his legacy, he’s going to have to work very hard to do it over these next two years.”