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The president will have dinner on April 10 with 12 Republican senators, including Sen. Johnny IsaksonJohnny IsaksonGOP senators wary of nuking filibuster SENATE: Republicans defy odds to keep majority A banner year for U.S. leadership on aid effectiveness MORE (R-Ga.), who is organizing the event.

The event is a sign that the president isn’t giving up on his increased outreach to Capitol Hill, which began earlier this month.

Obama called Isakson recently and asked him to organize the dinner, according to Joan Kirchner, the senator’s deputy chief of staff.

"The President called Sen. Isakson in the last 10 days saying that he thought the March 6 dinner was productive, and that he would like to have a second dinner to build on the first one, and that he would like Senator Isakson to invite some of his Republican colleagues," Kirchner said. "Sen. Isakson said he would be happy to do so."

In early March, Obama sat down with a dozen Republican senators for a two-hour meal at the Jefferson Hotel, where they talked the budget and a variety of other issues. The president will dine with a different group of senators on April 10.

Senators left the last meeting with Obama encouraged about the prospects for striking a deal on the deficit, calling the discussion “cordial” and “constructive.”