Clinton argues to Democratic officialdom that other factors should count, an unprovable assertion that she's more electable chief among them. But she undercut her own claim in Wednesday night's debate, answering "yes, yes, yes" when asked whether her rival could win the White House.
There's little if any public evidence the party's elite, the superdelegates who will attend the convention, are buying her argument anyway.
In the days since the surfacing of Obama's worst gaffe of the campaign - an observation that small town Americans are bitter folk who cling to religion and guns out of frustration - he has gained six convention superdelegates, to four for Clinton.
"I investigated and studied the context of the whole speech," said one of the six, Reggie Whitten of Oklahoma, who told Obama on Tuesday he would support him. "I think the comment was to some extent taken out of context and blown up, but I can tell you I think people in small towns have a lot of reason to be bitter," added Whitten, who grew up in Seminole, a town of 6,700.
Clinton leads in Pennsylvania polls in advance of Tuesday's primary there, with 158 convention delegates at stake. A victory is essential to her chances of winning the nomination, but far from sufficient. Instead, a triumph of any magnitude would instantly establish Indiana on May 6 as her next must-win state, particularly since her aides have privately signaled that defeat is likely in North Carolina on the same day.
Overall, Obama's delegate lead is 1,645-1,507. That masks an even larger advantage among those won in primaries and caucuses. There, his advantage is 1,414-1,250.
An additional 566 are at stake in the remaining contests in eight states, Guam and Puerto Rico before the primary season ends on June 3.
If Obama captures 53 percent of them, which is the share he has gained in contests to date, he would close out the primary season with at least 1,945 delegates, only 80 less than the total needed to clinch the nomination. If he and Clinton split the 566 evenly, he would still be within 100 of the number needed.
Clinton needs to win a forbidding 65 percent of the delegates in the remaining primaries to draw even with Obama in pledged delegates. It's a share she has achieved only once so far, in Arkansas, where her husband was governor for more than a decade.
Given the unyielding delegate math, Clinton has relied for weeks on forbearance from party leaders to sustain her challenge. And they are growing restless, eager for the epic nomination battle to end so Democrats can unify for the fall campaign against John McCain and the Republicans.
In fact, it's unlikely any other candidate could have survived as long without coming under overwhelming pressure to withdraw.
"There aren't many figures in American politics who could sustain 11 straight losses and hang into a race and raise $35 million," Obama said at The Associated Press annual meeting recently. "So in that sense she's unique, and the fact that former President Clinton is there, too, and the structure that he has of loyalty all across the country and the brand name that they have makes it very tough."
If he was bitter about it, he didn't show it.
Still, there are limits to how long party leaders will wait, given polls that show McCain has pulled even in the race for the White House.
New Jersey Gov. Jon Corzine, a Clinton supporter, said Friday she needs a big win in Pennsylvania, and a loss would be a "door closer."
Massachusetts Rep. Barney Frank, also a Clinton supporter, said recently that the candidate who trails in delegates after June 3 should quit the race. "Probably before that, once it becomes clear that one or the other is clearly - there's no realistic chance," he told the AP in an interview.
Frank's remarks were merely more pointed than when Senate Majority Leader Harry Reid said a few weeks ago that he hoped the race would be over by the end of June. Or when House Speaker Nancy Pelosi said she thought it would be a disservice to the party for the superdelegates to overturn the verdict of the primary voters.
Congressional leaders have their own reasons for wanting an end to the nominating campaign.
They are playing a different numbers game.
Obama and Clinton are focused on 2,025, the magic number of delegates.
But 218 is the number that matters most to Pelosi, the number of seats needed to assure a continued Democratic majority in the Congress that convenes in January. Reid has visions of 60, the probably unattainable number of seats that would allow a unified Democratic majority to break any Republican-led filibuster.
For now, they and other party officials have granted Clinton a little more time to make her case, and she takes every opportunity.
Eager to capitalize on Obama's comments about small town Americans, she announced the support last Tuesday of Bill Kennedy, a commissioner in Montana's sparsely populated Yellowstone County.
Unflustered, Obama countered 24 hours later with an announcement that 25 of the 35 Democratic members of the Legislature in predominantly rural South Dakota were for him.
"I know he's a Christian. I'm a Christian," said one of them, Dale Hargens, the state House leader.
He resides in Miller, S.D., population 1,650.
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EDITOR'S NOTE - David Espo covers politics for The Associated Press.
