President Obama is reaching out to Republicans. (AP)

Barack, party of 10?

In a rare move, President Obama has invited a group of Senate Republicans to dine with him Wednesday evening just up the street from the White House at the Jefferson Hotel, continuing a charm offensive aimed at striking a deal on fiscal issues with rank-and-file lawmakers instead of congressional leaders.

Senators and their aides confirmed that Wednesday's dinner list includes Sens. Tom Coburn (Okla.), John McCain (Ariz.), Pat Toomey (Pa.), Lindsey Graham (S.C.), Kelly Ayotte (N.H.), Dan Coats (Ind.), Bob Corker (Tenn.), John Hoeven (N.D.) and Ron Johnson (Wis.).

“I have a dog sled ready to go to be able to get there because of these terrible weather conditions that we’re under," McCain told reporters, and he confirmed his attendance.

“If they’ll feed me, I’m looking forward to it," Coburn said.

Turning serious, McCain and other senators said a serious discussion about fiscal issues is long overdue.

"We need to have this dialogue. I'm glad the president is doing it. I think it's very helpful that we have continued discussions," McCain said. "That's been my experience with other presidents, where you establish lines of communication."

“All of us are concerned about the fiscal state of the country," Ayotte added.

The guest list includes several senators not often involved in high-level bipartisan deal-making.

Asked what he would tell the president, Coats said: “My message is, Mr. President we’ve been dealing with short-term, buy-a-little-time stuff for two years now. Isn’t it time to reach some kind of big deal that puts this behind us and sets a course for the next 10 years, removes this dark cloud of uncertainty that’s hanging over the economy and gives us a clear path forward?"

Johnson, who joined the Senate in 2011, admitted that the dinner presented his first opportunity to have an extended conversation with the president.

“We have to start really addressing the 65 percent of the budget that’s generally off the table. We have to start seriously looking at Social Security and Medicare, these programs that simply aren’t going to be around if we don’t work to restructure them," he said.

Johnson said he believed the president was genuinely interested in holding serious conversations about fiscal issues -- and not just using Wednesday's dinner for political show.

“I’ll certainly give the president the benefit of the doubt," he said. "Hopefully he realizes how serious these problems are."

Obama also plans to visit Capitol Hill visit next week and meet with all four caucuses -- House Democrats and Republicans, Senate Democrats and Republicans.

In a statement, Senate Minority Leader Mitch McConnell (R-Ky.) said his conference would "welcome the president to the Capitol. And I appreciate he took my recommendation to hear from all of my members."

Mike Sommers, chief of staff for House Speaker John A. Boehner (R-Ohio), said Obama "has requested the opportunity to visit with our conference sometime next week to discuss various policy matters, and we are currently working to schedule that meeting. More details to follow."

On Tuesday, White House press secretary Jay Carney confirmed news reports that Obama is actively interested in “assembling a caucus of common sense and working with them to bring about a resolution to this challenge.”

The dinner follows a round of calls in recent days to several Republican senators, including Coburn, Graham and Corker, as well as Susan Collins (Maine), Rob Portman (Ohio) and Saxby Chambliss (Ga.).

Portman said Wednesday that he was not invited to the dinner. Nor was Sen. Johnny Isakson (R-Ga.), who seemed eager for a future invite. "I happen to socially like the president, so I think it’s a good idea," Isakson said about the dinner. He added: “I’m going to eat at home tonight.”

Collins confirmed she also didn't get a dinner invitation: “It must have been something I said in the conversation with the president," she joked. But she noted that she's responsible for hosting the Senate Republican lunch that Obama plans to attend next week.

“We will have Maine lobster and blueberry pie and Aroostook County potato chips," she said. "So no wonder he wants to come to my lunch -- even if he didn’t invite me to his dinner."

Also on Wednesday, Paul Ryan (R-Wis.), the House Budget Committee chairman and former GOP vice presidential candidate, told reporters that he had received a call from the president this week. Ryan declined to discuss the conversation.

Aaron Blake, Rosalind S. Helderman and Lori Montgomery contributed to this report. It has been updated.