Barack Obama is looking at May 20 as the end date for his Democratic primary run, even though that date won't seal the deal.

After a victory in North Carolina on Tuesday night and a closer-than-expected loss in Indiana, Obama campaign manager David Plouffe said that, based on calculations, Obama will win a majority of pledged delegates on May 20.

West Virginia votes Tuesday, and Kentucky and Oregon follow on the 20th. Hillary Clinton is expected to win West Virginia and Kentucky, while Obama is banking on victory in Oregon.

Clinton campaign chairman Terry McAuliffe told FOXNews.com on Thursday that the Obama camp's plan to declare victory based on a pledged delegate majority is "meaningless." He said that a candidate will need a majority of the pledged delegates and the unpledged superdelegates combined to be the true winner.

"Until you get to twenty-twenty-five or twenty-two-oh-nine, none of this matters," McAuliffe said, referring to the numbers being bandied about as the number of votes needed.

"In order to have a majority of the delegates seated at the national convention, that's how you get to become the nominee, not the pledged," McAuliffe said.

"If that's the case, take everyone of the superdelegates away from him, if he doesn't care about them."

The Democrats will have 3,253 pledged delegates and 796 superdelegates at the Democratic National Convention, if Michigan and Florida are excluded. Without those two states, the eventual Democratic nominee will need 2,025 delegates. If those states' delegations are ultimately seated, then a candidate will need 2,209 delegates to secure the nomination.

The Democratic National Committee decided to refuse to seat Michigan's 157 delegates and Florida's 211 delegates at the August convention because those states held their primaries ahead of Super Tuesday, Feb. 5, in violation of the party's rules.

Clinton won the primaries in both states, although neither she nor Obama campaigned in either state; Obama's name was not even on the ballot in Michigan.

Clinton wrote a letter to Obama Thursday urging him to support counting the delegations, warning of the general election consequences.

"One of the foremost principles of our party is that citizens be allowed to vote and that those votes be counted," she wrote. "That principle is not currently being applied to the nearly 2.5 million people who voted in primaries in Florida and Michigan. Whoever emerges as the Democratic nominee will be hamstrung in the general election if a fair and quick resolution is not reached that ensures that the voices of these voters are heard."

The Michigan DNC has offered a plan to divvy up its delegates, 69-59, essentially coming up with a middle ground between the two campaigns to have the state's delegates counted.

McAuliffe said he had not had time to review Michigan's plan to divide the delegates, but he can't imagine they'd be excluded from the convention.

"I think we ought to get all the delegates. [Obama] took his name off the ballot, deliberately, politically; it's a political decision which he made, which is fine, but they are going to give him all the uncommitted, I guess, John Edwards' and everyone else's," he said.

Clinton said Wednesday that the two states should be included, because excluding them "would haunt us in the fall election, in my opinion. So 2,209 or 10 is the number, and at some point one of us will get there," she said.

Still, even with Michigan and Florida included, the race is winding down. The final contests will be held in Montana and South Dakota on June 3, and McAuliffe said he expects the superdelegates to pledge their allegiances within weeks after that date.

"I think out of respect for the six upcoming contests, they want them to vote and after that they are going to move very quickly," he said. "They want to be part of the nominating process, so I think they all start moving very quickly and I think it's over in a couple weeks. It is never going to the convention."

Meanwhile, Clinton continues to make her argument for going forward, claiming she will be more electable than Obama against John McCain in November

"I'm winning Catholic voters and Hispanic voters and blue-collar voters and seniors -- the kind of people that Senator McCain will be fighting for in the general election," she said at a rally in Charleston, W.Va.

Taking a break from the campaign trail, Obama appeared on Capitol Hill Thursday, but denied that he was taking a victory lap when he headed over to the House side of the congressional campus and received rock-star treatment from pages and lawmakers alike.

"Everybody was very gracious," he told FOX News Radio. "As I said before, I think our goal is to bring the party together as soon as possible. But we still have contests remaining, so in no way am I taking this for granted.

"We're going to have to keep on working. Senator Clinton is a formidable candidate. She is very likely to win West Virginia and Kentucky, those are two states where she has insurmountable leads. We're going to spend some time there, but we are also going to be going to Oregon and Montana and South Dakota and Puerto Rico (June 1).

"But in the meantime, I just wanted to make sure that I gave an update not only to my supporters but those who are also trying to figure out what direction to go in," Obama said.