Senate Democrats are pivoting to throw their weight behind Rep. Joe Sestak, their newly minted nominee in the Pennsylvania race, and a coveted invitation to the Conference’s weekly lunch is among the welcoming gestures that Majority Leader Harry Reid (D-Nev.) is likely to make once the dust settles.

“I assume that he will be invited at some point, but no word yet on timing,” said Jim Manley, a spokesman for Reid, who publicly backed incumbent Sen. Arlen Specter in Tuesday’s hotly contested primary.

Senate Democrats, who hope to keep the seat in November, said Wednesday that they thought it would be appropriate for Reid to invite Sestak to introduce himself, talk about the race and make a pitch to them at a Conference lunch — an opportunity that other House Members and select Democratic challengers seeking Senate seats have been afforded in recent months.

Sestak pulled off an upset win over Republican-turned-Democrat Specter, despite the fact that the Senator was the party favorite and had White House support. Sestak said late last week that he would jump at the opportunity to attend a lunch.

“In a heartbeat, I’d go over,” he said. “I intend to work very well with those colleagues.”

But the situation is fraught with potential awkwardness given the bruising intraparty squabble that preceded Sestak’s win and the fact that Specter would likely be present at the lunch.

None of those dynamics was in play in March when Rep. Brad Ellsworth (D-Ind.) attended a Tuesday lunch or last May when Rep. Paul Hodes (D-N.H.) took Reid up on his invitation to travel across the Capitol to introduce himself and share “a little bit about politics in New Hampshire,” Hodes said.

Aides to Rep. Kendrick Meek, the Democratic Senate candidate in Florida, are working to schedule a time for the Congressman to attend a caucus lunch before the election, Meek campaign spokesman Adam Sharon said.

Ellsworth, Hodes and Meek are seeking open seats and did not have to engage in major primary fights.

Sestak, by contrast, picked off a 30-year veteran of the chamber who had the financial backing and public support of his colleagues right up until he was defeated.

The situation is made even more delicate because a theme of Sestak’s campaign was that Specter, who has been a reliable Democratic vote since his party defection last year, had fallen short for Pennsylvania. In so doing, Sestak’s campaign took on the tinge of anti-incumbency, a sentiment that Democrats are trying to tamp down in their effort to stave off GOP gains.

In an e-mail to supporters Wednesday, for example, Sestak touted his victory as triumph “over the establishment, over the status quo, even over Washington, D.C.”

National Republican Senatorial Committee Chairman John Cornyn (Texas) said the GOP would have an easy time poking holes in Sestak’s posture, noting his support in the House for major agenda items like health care and climate change.

“What’s pretty interesting is to watch Joe Sestak try to run like he’s a Washington outsider when he’s been here voting loyally with Nancy Pelosi’s agenda in almost lock step,” Cornyn said, adding that Democrats now “don’t have any choice” but to back Sestak.

Indeed, once the outcome was clear, Senate Democrats were quick to pivot toward Sestak, who they insisted was a strong candidate capable of beating Republican Pat Toomey in November.

Reid, who contributed $10,000 to Specter’s campaign through his leadership political committee, set the tone for that pivot Tuesday night, when he released a statement saying he and his colleagues would “wholeheartedly support Congressman Sestak as the Democratic nominee.”

Specter, who complicated matters for Senate Democrats on Wednesday when he did not return to the Capitol for a key procedural vote on the majority’s financial regulatory reform legislation, said Tuesday in an MSNBC interview that he too would support Sestak if he won the nomination.

Democratic Senatorial Campaign Committee Chairman Bob Menendez (N.J.) said he spoke to Sestak on Wednesday morning, adding, “He’s ready to fully engage with the DSCC, and our efforts to help him.” Reid generally consults with the DSCC when determining whether to invite a candidate to a Conference lunch.

Reid’s top lieutenant, Majority Whip Dick Durbin, vehemently disputed the idea that there would be any awkwardness associated with bringing Sestak into the fold. The Illinois Democrat said he personally would have no problem with Sestak attending a lunch.

“I wouldn’t be opposed to it at all,” he said. “I think that’s understandable.”

Durbin said now that “the people of Pennsylvania had spoken,” he thought Sestak would have “the full support” of the Democratic Conference, predicting that Sestak would also have no trouble raking in money from his Senate colleagues who had an interest in staving off a Republican pickup. Durbin said he wrote Sestak on Wednesday morning offering to help him in any way he could.

“He ran a spirited and good campaign, and the voters chose him,” Durbin said. “That’s the nature of this business.”

Sestak also rebuffed the idea that it would be awkward for him to attend a lunch or to otherwise elicit support from Democratic Senators after the primary.

“To me, this is not personal,” he said on May 13. “I knew when I got in to run against the Democratic establishment, the challenges there would be.”

Sestak went as far as to indicate that he had behind-the-scenes support in the Senate even before he won the nomination, saying a few Senators — he declined to reveal who — would “call every so often” during the primary campaign to “see how things were going.”

Freshman Sen. Mark Udall (D-Colo.), who spoke to the Conference in 2008 when he was a House Member seeking to pick up a seat that had belonged to retiring Republican Wayne Allard, described the appearance — which, in his case, consisted of a two- or three-minute presentation with no question-and-answer period — as an “opportunity to show people what you might be like as a colleague” and “to make your case for support from the caucus.”

“I’ve got three minutes to tell them how I’m going to win, what’s important to me, to maybe tell a story that connects,” Udall said. “It’s an important signal that is sent to the caucus. Not everybody gets an invitation in every race.”