WASHINGTON – They’ve spent thousands of hours seeking the 2012 Republican presidential nomination. Giving speeches. Shaking hands. Raising money. But perhaps nothing has mattered as much as the roughly 15 hours that the GOP candidates have spent onstage debating one another.

The eight debates — from a May debut in South Carolina through the latest Tuesday night in Nevada — have had an unusually important impact on the race. They’ve propelled candidate after candidate to the top tier, knocked some down and helped one maintain a consistent if weak claim on top status.

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At the presidential candidate debate Tuesday in Las Vegas, Republican Herman Cain, left, watches former Massachusetts Gov. Mitt Romney, center, spar with Texas Gov. Rick Perry. The Associated Press

The swings of fortune raised the stakes of the debates, particularly as the campaign marches toward the start of voting in less than three months. That now-or-never attitude helped drive the increasingly nasty tone of Tuesday’s debate in Las Vegas, one that prompted Newt Gingrich to warn that “maximizing bickering is probably not the road to the White House.”

The bottom line heading toward winter voting: Former Massachusetts Gov. Mitt Romney holds a share of the lead in national polls, a share of the lead in Iowa — the first state to hold precinct caucuses — and a large lead in New Hampshire, the first state to vote in a primary.

“We’ve learned two essential things from the debates,” said Dan Schnur, a veteran of John McCain’s 2000 presidential campaign and now director of the Jesse M. Unruh Institute of Politics at the University of Southern California.

“Romney, if anything, has strengthened his status as a front-runner,” Schnur said. “And, if anything, the yearning among conservatives for an anti-Romney candidate keeps getting stronger.”

While Romney consistently wins the support of about a quarter of likely Republican primary voters, three out of four Republicans continue to watch debate after debate, looking for someone else. Right now, they fancy businessman Herman Cain. But as the past few months have shown, that could change before the next debate rolls around on Nov. 9 in Michigan.

“Most of them have been found lacking. First one, then another, then another, have shot to the top, then fallen away precipitously,” said Republican pollster Whit Ayres. “The debates have been the major way for Republicans around the country to size up their field.”

Particularly for candidates without much money, the debates are a free way to reach millions.

Rep. Michele Bachmann used a standout performance in an early debate to seize momentum in Iowa, winning a straw poll and driving fellow Minnesotan Tim Pawlenty from the race. She faded when Texas Gov. Rick Perry jumped into the race and soared quickly to the top of the polls. Then he stumbled through his first three debates and watched his support plummet.

Next the debates lifted Cain, a former corporate CEO with almost no campaign offstage. He used the debate exposure to trumpet his resume as a CEO and his 9-9-9 tax plan, jumping to a win in a straw poll of Florida Republicans and a surge in the polls.

Cain’s surge may have ended with Tuesday’s debate, when every one of his rivals ripped his tax plan.

Former House Speaker Newt Gingrich, whose campaign fell on hard times over the summer from big spending and a mass staff resignation, has shined as the ideas man in debates since then. Tuesday night he sometimes looked like the grown-up onstage, rising above the petty bickering of his rivals. He may be setting himself up for a second wind.

“Newt is back,” said Greg Mueller, a conservative strategist. “We might see him pick up more in the polls.”

And then there’s Romney. A wooden performer when he ran four years ago, Romney has been quick on his feet, firm in his focus on the economy and even glib in the debates this time.

“Romney has not yet put this away. There is still an appetite for an alternative,” said Ayres. “If someone emerges as a serious and credible alternative, they could give him a run for his money. If not, then Gov. Romney will be the nominee.”

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