(CNN) -- Sen. Barack Obama said that Democrats will know their presidential nominee after the final two primary states vote next week -- and that in his view, the general election campaign officially will begin.

Sen. Barack Obama says remaining superdelegates likely will make their decisons quickly after next week's contests.

"After Tuesday, we will [have a clear idea]. I think Saturday will be important, put the Michigan-Florida issue behind us," Obama said Wednesday on a flight from Denver, Colorado, to Chicago, Illinois.

The party's Rules and Bylaws Committee meets this weekend to consider what to do about delegations from Florida and Michigan, which broke ranks to hold primaries earlier than party rules allowed.

"We've got three contests in succession. And at that point, all the information will be in," Obama said, referring to Sunday's vote in Puerto Rico and Tuesday's primaries in Montana and South Dakota.

"I suspect that you know whatever remaining superdelegates will make their decisions pretty quickly after that."

By most tangible measures, the general election fight between Obama and the presumptive Republican nominee, Sen. John McCain, has begun. The two men and their campaigns tangle almost daily over issues of policy, politics and character, in which Sen. Hillary Clinton does not rate a mention.

The Republican National Committee has focused its full firepower on Obama for months, and this week, its Democratic counterpart took on McCain after his team accused Obama of campaign trail gaffes and distortions.

And the Obama campaign, unlike Clinton's, has embarked on the first stages of an ambitious strategy for the general election: going on a hiring spree with an eye toward a national campaign infrastructure, launching a massive 50-state voter registration drive, and regularly sending the senator from Illinois to crucial fall swing states that have held presidential primaries.

Obama returned home to Chicago from Denver late Wednesday after a three-day campaign swing in New Mexico, Nevada and Colorado. Those are all considered battleground or swing states up for grabs in November.

Obama said that the date when he would be able to claim the nomination depends on the Democratic National Committee's Saturday decision on the seating of the Florida and Michigan delegations -- but that once he claims the required number of delegates, he will be the winner.

CNN.com/Live will stream live coverage of the meeting from start to finish on Saturday.

By CNN's count, Obama is 48 delegates shy of the 2,026 needed to clinch the Democratic presidential nomination and 198 delegates ahead of Clinton. Should the rules committee decide to seat those additional delegates, the number required for the nomination would rise to reflect that fact.

Asked whether the general election campaign officially starts after next Tuesday's votes, he said it did.

"I am sure we will have discussions with Sen. Clinton and her team. ... It is technically not over until we have the number of delegates that are needed to secure the nomination," he said. "Once we have that number, then we'll focus on the general election."

Clinton seemed to sound a note of resignation on her campaign plane as she made her way to Sioux Falls, South Dakota.

"You know, I feel so good about the process. I feel that this has been a really positive, productive primary season in so many ways," she said. "And, you know, I put some of that in the memo [sent to superdelegates Wednesday], about the numbers of people that have been brought in."

Two members of the Rules and Bylaws Committee said Wednesday that Michigan and Florida probably will be restored to half their original delegate strength. Together, Michigan and Florida have 368 delegates.

Clinton and her supporters have pressed for a compromise that seats as many delegates from the two states as possible. Watch more on the Democrats' dilemma »

"There is one number that we are going to be satisfied with, and that is 2.3 million people having their votes counted," Clinton supporter and rules committee member Tina Flournoy said Wednesday.

About 600,000 people voted in Michigan and about 1.7 million in Florida.

The DNC stripped the two states of delegates for violating party rules by scheduling their primaries too early in the cycle. Both candidates agreed not to campaign in the two states, and Obama's name did not even appear on Michigan's ballot.

Clinton won both January primaries. Watch Clinton say she's the best candidate to beat McCain »

The Obama campaign has said it is willing to concede an advantage to Clinton on how Michigan and Florida delegates are seated, portraying its position as a gesture to party unity.

Several lawsuits have been filed to force the seating of the full Florida delegation, so far unsuccessfully.

"Any compromise is going to benefit Sen. Clinton," Obama strategist David Plouffe said Wednesday. "We're hoping there can be some reasonable resolution on Saturday that can allow us to move to the general election."

Obama downplayed concerns over legal action and other lingering legacies of a bitterly contested campaign, saying Wednesday that a contentious convention was "true of every convention" and "fairly standard fare."

"If we've got the number of delegates to secure the nomination, then I'm the nominee. If we're short of that, then we'll have more work to do. But once we achieve it, then I think we'll be the nominee," Obama said.

"We are only a few days away. We have waited this long. We can wait a while longer."

House Speaker Nancy Pelosi signaled increasing willingness to use her influence to end uncertainty over the nomination well before the national convention in August.

Pelosi told the San Francisco Chronicle on Wednesday that she expects the nominee to be settled in the week following the final primaries.

But she told the newspaper that if the nominee is still in question by the end of June, she "will step in" to halt the standoff.

CNN's Paul Steinhauser and Ed Hornick contributed to this report.

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