Barack Obama’s campaign began to reclaim lost momentum Saturday, beating Hillary Clinton by double digits in the Wyoming caucuses on the road to more critical upcoming contests.

The caucuses only offered 12 total delegates, but both candidates campaigned there and drew rare attention to the state as well as historic turnout.

With 96 percent of precincts reporting, Obama had 59 percent to Clinton’s 40 percent.

“It’s a big win,” Obama spokesman Robert Gibbs said. “It adds to our momentum, it adds to our delegate lead on the road to becoming the nominee.”

Associated Press tallies showed the delegate bonus was negligible. Obama was projected to win seven delegates to Clinton’s five.

The candidates were already shifting their attention toward the Mississippi primary Tuesday, which offers 33 delegates. Polls consistently show Obama ahead in the state, but Clinton stopped by the state Friday to campaign. Bill Clinton had four stops in Mississippi Saturday.

After Clinton disrupted Obama’s month-long winning streak Tuesday with victories in Texas, Ohio and Rhode Island, the onus was on Obama to win Wyoming. Obama had prevailed in 12 of the 15 caucuses so far and was generally favored in the state, but there were no public polls beforehand.

Obama got a big bump Saturday from Albany County, which contains the University of Wyoming. The state Democratic Party reported 75 percent of caucus-goers there went for Obama.

“They mounted a very aggressive effort on the ground,” Obama campaign manager David Plouffe said of the Clinton push in Wyoming. “So this is a very important win for us.”

However, Clinton downplayed expectations in Wyoming ahead of time, and campaign manager Maggie Williams issued a statement Saturday claiming the contest was a virtual draw.

“We are thrilled with this near split in delegates and are grateful to the people of Wyoming for their support,” she said. “Although the Obama campaign predicted victory in Wyoming weeks ago, we worked hard to present Senator Clinton’s vision to the caucus-goers and we thank them for turning out today.”

Clinton spokeswoman Hilary Perry told FOX News that the next big contest for them is Pennsylvania, which votes April 22 and offers 158 delegates. It is the biggest prize remaining on the election calendar, and polls show Clinton ahead in the state.

Obama still holds a comfortable lead in delegates. After Saturday’s caucuses, the count stood at 1,578 for Obama and 1,468 for Clinton. It takes 2,025 to win.

With the almost unprecedented political attention, turnout was high in Wyoming as thousands of voters deluged caucus sites. Wyoming Democrats hadn’t played this big a role in 50 years. Republicans have 136,000 registered voters in the state, compared with 59,000 Democrats.

Click here to see photos from the Wyoming caucuses.

“We just don’t even know how to act,” said Wyoming state Rep. Mary Gilmore, a Clinton supporter. “It’s fabulous.”

But party officials were struggling with how to handle the overflow crowds. The start of the Converse County caucus was delayed due to long lines.

In Cheyenne, scores of late arrivers were turned away when party officials stopped allowing people to get in line at 11 a.m. EST.

In the Cheyenne Civic Center, officials were expecting 500 caucus-goers, but 2,500 showed up early in the day.

In Casper, hundreds were lined up at the site of the Natrona County caucus. The location was a hotel meeting room with a capacity of 500. Some 7,700 registered Democrats live in the county.

“Wyoming is usually not thought of as a momentum state, but it happens to fall on a calendar at a good time for both of them,” said Kenneth Bickers, political science chair at the University of Colorado who is an expert in Western politics. “Both of them need to be able to claim a victory. Both of them need whatever delegates they can get to help move their delegate count in a positive direction.”

Only in the last few weeks did the campaigns step up their presence in Wyoming, opening offices and calling voters and sending mailers. The first visit came Thursday, when former President Clinton made three appearances in Wyoming.

The candidates followed on Friday. Clinton held town-hall meetings in Casper and Cheyenne. Obama held a town hall in Casper and a rally in Laramie at the University of Wyoming, counting on support from college students. Obama had been running television and radio ads in the state, while Clinton had been running radio ads.

The candidates had no public events Saturday, but traded barbs via campaign memos about Obama’s Iraq war plan. For the second day in a row, Clinton’s campaign ridiculed Obama for his former foreign policy adviser’s remarks to the BBC that his plan to withdraw troops was flexible.

“And if you can’t trust Senator Obama’s words, what’s left?” the Clinton memo said.

The Obama camp hit back with a memo claiming Clinton still trying to attack him with the “kitchen sink strategy.”

The memo said Clinton “knows full well” that Obama’s plan is to withdraw troops immediately while retaining the flexibility to do it “in a way that ensures the safety and security of our troops.”

Wyoming’s top Democrat — Gov. Dave Freudenthal — declined to endorse either candidate, saying they haven’t talked enough about Western issues. State party chair John Millin is backing Obama, while former Gov. Mike Sullivan has endorsed Clinton.

Although the win in Wyoming may not persuade many superdelegates, it is one more prize for Obama as he makes his case for the nomination.

Wyoming Democrats have relished the attention, harkening back to the 1960 Democratic National Convention when the state’s delegation cast 15 votes that pushed Sen. John F. Kennedy over the top for the nomination.

Party spokesman Bill Luckett said he’s never seen Wyoming Democrats in such a frenzy.

“People are really excited about this year and the role Wyoming is playing,” Luckett said.

FOX News’ Aaron Bruns and Bonney Kapp and The Associated Press contributed to this report.