Editor's note: David Gergen is a senior political analyst for CNN and has been an adviser to four U.S. presidents. He is a professor of public service and director of the Center for Public Leadership at Harvard University's Kennedy School of Government.

(CNN) -- The stakes are growing ever higher on deficit negotiations in Washington. And as they do, the politics are becoming ever more treacherous, especially for Democrats.

When President Barack Obama gathered with congressional leaders Thursday at the White House, almost everyone there agreed that it would be good to strike a grand bargain reducing deficits by $4 trillion over some 10 years. If you worry -- as I do -- that the country is sliding toward a debt crisis, their enthusiasm for a mega-deal is welcome news.

House Speaker John Boehner told his Republican caucus Thursday morning that he thought the chances of reaching a big agreement had risen to 50-50. While little bargaining went on at the White House meeting, Boehner reportedly left still believing those odds.

But a closer look suggests the chances of getting there seem much lower. Success rests heavily upon either the Republicans or Democrats caving in on their public positions -- and in the case of Democrats, not one but two caves. It is hard to imagine either party giving in enough.

Leading Democrats in Congress have long argued they will agree to massive spending cuts only if Republicans agree to tax increases. Lately, Democrats have been floating the idea that the GOP should agree to as much as $1 trillion in revenue increases as part of the $4 trillion package. But Republicans are virtually united in opposing any tax increases, much less $1 trillion. It is almost impossible to foresee them backing down now, no matter how many sweeteners they are offered.

In fact, what Republicans actually hope is that the Democrats will once again give in, led there by the president. That is what happened last year when Obama persuaded his party to give up on tax increases on the affluent and instead continue the Bush tax cuts for everyone. Boehner's 50-50 estimate appears to rest on the chance that a similar scenario will unfold now -- that Obama will cajole his party into big-time compromises.

But that possibility is exactly why so many liberal Democrats are angry. They worry Obama is once again surrendering before he has even begun to fight. And in the process, they think, he may be undermining their chances of holding the Senate and regaining the House in 2012.

It's easy to understand why they are so unhappy. They believe that the GOP handed them a great cudgel for next year's elections when House Republicans voted in favor of the Paul Ryan deficit plan, including its bold but controversial plan to transform Medicare. House Minority Leader Nancy Pelosi recently proclaimed that there would be three big issues in 2012: Medicare, Medicare and Medicare.

Democrats are itching to run as protectors of Medicare and Social Security; they just love to argue that the mean, ol' Republicans want to balance the budget on the backs of the elderly and the poor while preserving tax breaks for fat cats. That theme has played well for them, so far.

Now, from their point of view, along comes Obama proposing Medicare cuts and even putting Social Security cuts in play as part of a mega-deal. Democrats in Congress complain bitterly that not only did he not consult them in advance but he could now compromise the heart and soul of their 2012 campaigns.

And what does he get from Republicans in return? Not a damn thing, they say -- just some billowy talk. One Democratic partisan said privately that he still likes Obama but he never, ever wants him to negotiate on his behalf for anything.

In effect, as they recognize, Democrats on Capitol Hill may be facing a double vise. Their own president is asking that they be willing to cut back entitlement programs. And there is a very real possibility that if Republicans hold tough on significant tax increases, the White House may be so hungry for a deal that Hill Democrats will be asked to accept that, too. That's two caves too many for a lot of Democrats.

From afar, it appears that Obama is now operating on a different political calculus for 2012 than his congressional party. He needs to win over independents -- and a mega-deal reducing the deficits could be a huge plus for him. But congressional Democrats need to have a fired-up base, and that means not caving in on entitlements, especially when there is so little in return. Even if Obama is just posturing, talking big now so he gets credit for trying, his strategy is not a happy one for the left.

Putting all of this together, the odds seem long -- certainly below 50-50 -- that the White House and Congress will agree on a mega-deal, as good as it would be for the country. Instead, it appears far more likely they will eventually settle upon a short-term fix. Nobody will be very happy -- and some Democrats will still be steaming.

The opinions expressed in this commentary are solely those of David Gergen.