With party unity crucial to Democrats’ hopes for passing significant legislation before the midterm elections, Arlen Specter’s primary loss could pose a new problem for the White House.

The Senate could vote on any number of crucial bills before the midterms, including a new jobs bill, immigration reform, climate-change legislation, and a final financial-reform package, making Specter’s continuing support more important than ever. But several longtime friends and associates tell The Daily Beast that without a primary challenge to pressure him, the veteran senator--a famously prickly character whose temper has earned him the nickname "Snarlin' Arlen"—may shift to the right.

“In my opinion, I think this will simply make Specter more comfortable in doing what he thinks is right, as opposed to doing things Obama wants him to do,” said Morton Klein.

When Specter announced his switch to the Democratic Party last year, he made clear in his first Meet the Press appearance that he would not be a “ loyal Democrat,” even touting his “no” vote on President Obama’s budget and his opposition to a public option for health-care reform and the reconciliation procedure that ultimately would end up being used to secure the legislation’s passage. But, facing a primary challenge from the left, he later reversed his stand on a public option and voted for a reconciliation package on health care as well.

In addition to Specter’s shifting policy views on key issues, polling guru Nate Silver notes that the senator began to vote with the Democrats much more often after Rep. Joe Sestak announced a primary challenge, eventually toeing the party line 96.1 percent of the time, according to The Washington Post.

Dave Urban, a lobbyist for American Continental Group who previously worked as the senator’s chief of staff, said Specter’s position on Elena Kagan’s confirmation to the Supreme Court could be a key test vote in gauging his continued loyalty to the party’s agenda. Specter voted against Kagan’s confirmation as solicitor general while he was a Republican, saying in a statement that she failed to provide clear enough answers to his questions, and he has not committed to supporting her for the Supreme Court.

Specter met with Kagan this month, before the primary, and said Obama’s nominee was “very forthcoming” in their discussion. On Wednesday, he released a letter detailing three cases dealing with jurisdictional issues that he intended to question her on in upcoming hearings. He has shown a maverick streak on Supreme Court votes in the past, bucking the Reagan administration by opposing Robert Bork in 1987, only to infuriate Democrats with his contentious questioning of Anita Hill during the Clarence Thomas hearings in 1991.

“That’s the vote to really watch if you’re an Arlen Specter observer,” Urban said. “It’s a big vote and he obviously had some concerns the first time for solicitor general. So have those concerns been alleviated, or do they remain?”

Roger Stone, a GOP consultant who worked on Specter’s first successful Senate run in 1980 and chaired his 1996 presidential campaign, told The Daily Beast that he expected Specter to buck his party on the Supreme Court pick following his failed primary.

“It all boils down to how he votes on Kagan, and if I were a betting man, I’d bet he votes against her,” Stone said. “He voted against her before, so it would be consistent with his previous position. And given the way the Obama White House double-crossed him by not going to Philadelphia the final weekend and leaking two days before that they’re bracing for a Specter loss… that’s a treacherous Chicago style of politics.”

Specter’s final days on the campaign trail, as Stone noted, introduced new tensions with the White House. Obama supported Specter’s candidacy with an endorsement and appearances in ads and robo-calls, but their marriage ended on a sour note when the president failed to make a last-minute appearance in Pennsylvania to rally voters in a tight race. In an additional poke in the eye, CBS’ Face the Nation host Bob Schieffer reported ahead of the election that White House sources were “preparing for a Specter loss here, and that the president doesn’t want to be associated with that.” Nonetheless, Specter told CBS on the eve of the vote that the White House has “done everything we’ve asked them to do.”

Morton Klein, head of the Zionist Organization of America and a longtime ally of Specter, said a perceived White House snub could provide a pretext for a revolt by the senator.

“In my opinion, I think this will simply make Specter more comfortable in doing what he thinks is right, as opposed to doing things Obama wants him to do,” Klein said.

Then again, Specter may surprise observers, and show himself more of a team player than expected during his final months in the Senate. On Tuesday, the defeated incumbent extended Sestak a notable courtesy by introducing him at the Senate Democrats' weekly caucus lunch.

Asked whether the senator’s voting pattern might change in his remaining months, a spokeswoman for Specter, Kate Kelly, said: “Senator Specter will continue to examine each issue on an individual basis on the merits.”

Benjamin Sarlin is Washington correspondent for The Daily Beast. He previously covered New York City politics for The New York Sun and has worked for talkingpointsmemo.com.