Senator Barack Obama emerged from Tuesday’s primaries leading Senator Hillary Rodham Clinton by more than 100 delegates, a small but significant advantage that Democrats said would be difficult for Mrs. Clinton to make up in the remaining contests in the presidential nomination battle.
Neither candidate is expected to win the 2,025 pledged delegates needed to claim the nomination by the time the voting ends in June. But Mr. Obama’s campaign began making a case in earnest on Wednesday that if he maintained his edge in delegates won in primaries and caucuses, he would have the strongest claim to the backing of the 796 elected Democrats and party leaders known as superdelegates who are free to vote as they choose and who now stand to determine the outcome.
Mrs. Clinton’s aides said she could still pull out a victory with victories in the biggest primaries still to come, including Ohio and Texas next month. But Mr. Obama’s clear lead in delegates allocated by the votes in nominating contests is one of a number of challenges facing her after a string of defeats in which Mr. Obama not only ran up big popular vote margins but also made inroads among the types of voters she had most been counting on, including women and lower-income people.
Should the cracks in her support among those groups show up in Ohio and Texas as well, it could undermine her hopes that those states will halt Mr. Obama’s momentum and allow her to claim dominance in many of the biggest primary battlegrounds.
With every delegate precious, Mrs. Clinton’s advisers also made it clear that they were prepared to take a number of potentially incendiary steps to build up Mrs. Clinton’s count. Top among these, her aides said, is pressing for Democrats to seat the disputed delegations from Florida and Michigan, who held their primaries in January in defiance of a Democratic Party rules.
Mrs. Clinton won more votes than Mr. Obama in both states, though both candidates technically abided by pledges not to campaign actively there.
Mr. Obama’s aides reiterated their opposition to allowing Mrs. Clinton to claim a proportional share of the delegates from the voting in those states. The prospect of a fight over seating the Florida and Michigan delegations has already exposed deep divisions within the party.
Julian Bond, the head of the National Association for the Advancement of Colored People, called for the delegates to be seated, saying failure to do so would amount to disenfranchising minority voters in those states. But on Wednesday, such a move was denounced by the Rev. Al Sharpton of New York, who said many people in those states did not go the polls because they assumed their votes would not count.
Mrs. Clinton’s advisers acknowledged that it would be difficult for her to catch up in the race for pledged delegates even if she succeeded in winning Ohio and Texas in three weeks and Pennsylvania in April. They said the Democratic Party’s rules, which award delegates relatively evenly among the candidates based on the proportion of the vote they receive, would require her to win by huge margins in those states to match Mr. Obama in delegates won through voting.
The delegate math set up a new front in the battle for the party’s presidential nomination, one based on competing views of how the party leaders and elected officials whose vote will determine the outcome should make their decisions.
Mrs. Clinton’s aides said the delegates should make their decision based on who they thought would be the stronger candidate and president. Mr. Obama argues that they should follow the will of the Democratic Party as expressed in the primary and caucuses — meaning the candidate with the most delegates from the voting.
Mr. Obama’s aides said they hoped to end the voting season with a delegate lead of more than 100, which they would seek to portray as a decisive affirmation by Democratic primary voters of Mr. Obama’s candidacy. Mrs. Clinton’s advisers said they were looking to bring the margin down significantly below 100 in hope of arguing that the result was too close for delegates to consider in deciding how to vote.
Much for Mrs. Clinton depends on shoring up her support in the portions of the electorate — including women, low- and middle-income voters and Hispanics — that have provided her with victories in key states.
“Hillary does better with blue-collar voters, working-class voters, union members,” said Senator Sherrod Brown, the Ohio Democrat who has not endorsed anyone in the race. “Barack does better among African-Americans and younger voters and upper-income voters. If that holds, Ohio tilts toward Hillary.”
Mrs. Clinton’s campaign showed signs of being buffeted by conflicting forces as it sought to grapple with a dwindling number of options. Mrs. Clinton’s advisers, after some discussion about whether to focus exclusively on Ohio and Texas for the next three weeks, finally decided to send her for three days this week to Wisconsin, which votes next Tuesday.
Mrs. Clinton’s advisers said that they did not think she could win there but that they had concluded at this point they could not afford to leave any delegates on the table or allow Mr. Obama to run up another big margin of victory in the popular vote.
Mrs. Clinton’s aides said they would also argue to superdelegates that they should give less deference to a lead from Mr. Obama because much of that had been built up in states where there were caucuses, which tend to attract far fewer voters than primaries, where Mrs. Clinton has tended to do better than she has done in caucuses.
“I think for superdelegates, the quality of where the win comes from should matter in terms of making a judgment about who might be the best general election candidate,” said Mark Penn, Mrs. Clinton’s senior campaign adviser.
The final Democratic primary contests are in early June; Montana and South Dakota vote June 3, and Puerto Rico four days later. It would then be almost three months until the Democratic convention, a period in which, if enough superdelegates have not expressed a firm preference to decide the outcome, the party could face a period of intense horse trading or worse.
Meanwhile, the likely Republican nominee, Senator John McCain of Arizona, would have a long period to rally his fractious party to his side and hone his attacks on the Democrats.
A delegate count by The New York Times, including projections from caucuses where delegates have not yet been chosen, showed Mr. Obama with a 113-delegate lead over Mrs. Clinton: 1,095 to 982.
Delegate counts by other news organizations and by the campaigns showed somewhat different results, reflecting the difficulty of trying to make exact delegate counts at this point in the process. The figures do not include superdelegates.
Mrs. Obama’s campaign said that he had a lead of 1,139 to 1,003; by the count of the Clinton campaign organization, Mr. Obama was doing even better: 1,141 to 1,004 for Mrs. Clinton.
There are 1,082 delegates left to be selected.
By any measure, Mr. Obama is in a much stronger position on Wednesday than he was just a few days ago and in a significantly stronger position than Mrs. Clinton thought he would be at this point. That is because Mr. Obama not only won a series of states, but also won them by large margins — over 20 percentage points — so that he began picking up extra delegates and opening a lead on Mrs. Clinton.
And that is the problem for Mrs. Clinton going forward. If these were winner-take-all states, Mrs. Clinton could pick up 389 delegates in Texas and Ohio on March 4. Now she would have to beat Mr. Obama by more than 20 percentage points in order to pick up a majority of delegates in both states.
“We don’t think our lead will drop below 100 delegates,” David Plouffe, Mr. Obama’s campaign manager, said in an interview. “The math is the math.”
Mr. Plouffe said by his count, Mr. Obama had won 14 states by a margin of over 20 percentage points or more; Mrs. Clinton has won two states by that margin.
Mr. Penn said the Clinton campaign believed that it could mitigate the losses she suffered by winning in Ohio, Texas and Pennsylvania. In addition to whatever demographic advantage she might have in Ohio, Mrs. Clinton enjoys the support of the governor, Ted Strickland.
“They are working very hard on her behalf,” said Chris Redfern, the party chairman, who is neutral in the race. “It’s not one of those ‘we show up the last week and do a press conference’ things.”
In Texas, Mr. Penn said Mrs. Clinton would be helped by the Latino vote — which he said could ultimately be as much as 40 percent of the electorate.
But Mrs. Clinton faces another problem there in the form of that state’s unusual delegation allocation rules. Delegates are allocated to state senatorial districts based on Democratic voter turn-out in the last election. Bruce Buchanan, a professor of political science at the University of Texas at Austin, noted that in the last election, turnout was low in predominantly Hispanic districts and unusually high in urban African-American districts.
That means more delegates will be available in districts that, based on the results so far, could be expected to go heavily for Mr. Obama. Mrs. Clinton, Dr. Buchanan said, “has got her work cut out for her.”