Former White House Chief of Staff Erskine Bowles and ex-Sen. Alan Simpson, R-Wyo., stormed Capitol Hill on Wednesday, but don’t count on their ill-fated bipartisan debt reduction plan to make a comeback, too.

The Simpson-Bowles plan, with its calls for lowering tax rates while ending deductions and reforming entitlements, has been roundly panned by leaders on both sides since it was shot down almost two years ago by the very fiscal commission that produced it.

The plan’s namesakes, on the other hand, have withstood the withering criticisms of their blueprint and still hold up, particularly in the media, as standard-bearers of bipartisanship.

And that, in spite of everything, is why they were invited to the Capitol on Wednesday.

“They’re red-hot right now. Members want their pictures taken with them,” said Rep. Jim Cooper, D-Tenn., an early and ardent evangelist for the plan they produced.

Cooper met with the duo Wednesday afternoon along with a bipartisan group of congressmen, many of whom were among the 38 members who voted for a budget modeled after Simpson-Bowles last year — they have taken to calling themselves the “Brave 38.”

That came after Bowles and Simpson held a press availability with House Democratic leaders and Bowles met behind closed doors with Republican House leaders and a group of CEOs dedicated to debt reduction.

That Bowles and Simpson have seen a surge in popularity on Capitol Hill since the election, though, is less a function of their plan gaining traction and more about what they symbolize.

Leaders hoping to be perceived as more open to a bipartisan deal — and in effect hoping to gain an eventual upper hand in negotiations — were eager to be seen meeting with one or both of the men.

“The plan symbolizes something greater than the specifics of the plan; the plan symbolizes compromise,” a GOP leadership aide said. “At some point, I do think the speaker and president are going to get in a room, but a significant part of leverage on both sides comes from the public perception of the debate.”

Bowles acknowledged that the plan he and Simpson labored over and have long touted is still a tough sell on Capitol Hill. Coming out of a meeting with GOP leaders, he said the ideals of Simpson-Bowles are more important then the specifics.

“I think a balanced approach is a good starting point, and that’s what we’ve got to have. What we put out was a balanced approach, but it’s only one plan. There are lots of ways to get there,” he said. “I think if you ask anybody, from the minority leader to the speaker, if there are more people that favor the kind of balanced approach that we presented, they say, ‘Yes.’”

The problem remains, however, that while most lawmakers call for a balanced deal, they back away at the mention of specifics, said Rep. Peter Welch, D-Vt.

“Their plan has lots to criticize, but it has the one structural approach that everyone knows ultimately will be necessary,” he said. “The challenge now is to get specific.”

Indeed, Bowles said Wednesday after meetings that he sees no give from Democrats in the area of entitlement reform and similarly none from Republicans in raising tax rates.

Still, Cooper said the chances that a Simpson-Bowles type of plan can pass have “gone up dramatically,” saying “the whole world has changed” since he and Rep. Steven C. LaTourette, R-Ohio, brought the budget to the floor last year.

“Simpson and Bowles were never wedded to every detail of their plan,” he said. “For the rest of us, it’s one of the few bipartisan ways to solve the problem.”

Correction, Nov. 28

An earlier version of this story incorrectly stated how Rep. Peter Welch, D-Vt., voted on a budget package modeled after the Simpson-Bowles deficit-reduction package. Welch did not vote for the package.