WASHINGTON - It took three hours and 33,000 words, including 54 “jobs,” and one “Big Bird.” But the first two debates revealed something that long months of speechifying had not: two campaigns, stripped down to their core arguments.

These were the things the four candidates chose to talk about: Republican Mitt Romney and his running mate, Paul Ryan, focused largely on their policy agenda, which was dominated by things they wanted to roll back – the health care law, the Dodd-Frank financial regulations, income-tax rates.

The Democrats tended to cast the election less as a choice between ideas and more as a choice between people. President Obama and Vice President Joe Biden stressed their personal credibility, citing their work in office, and the lessons of their upbringing. They attacked Romney and Ryan as aloof and uncaring.

“Look, folks, use your common sense,” Biden said Thursday night – talking about Social Security, but also compressing the Democratic appeal into two sentences. “Who do you trust on this?”

After months of campaigning and hundreds of millions spent on a barrage of television ads, the debates have come to define – and may well determine – the race for the presidency. The slow and steady gains that Obama had consolidated in September have been all but erased by his poor showing in the first debate. Both sides were pleased with the performances by Biden and Ryan, but the sole vice presidential debate does not appear to have fundamentally changed the race.

Next up is a debate today at Hofstra University on Long Island, N.Y., where Obama and Romney will face audience questions in a town hall format. The final debate is Monday in Florida, and will focus on foreign policy.

The importance of those showdowns was underscored by the candidates’ weekend plans. Both were in critical swing states – Romney in Columbus, Ohio, and Obama in Williamsburg, Va., – but both spent time holed up in hotel rooms practicing for today.

Even if the first debates left the race itself muddled, they served to clarify the messages at each campaign’s heart.

That’s because, for once, there were time limits. Some issues had to be left out. None of the candidates, for instance, has mentioned climate change, immigration or same-sex marriage so far.

And – four years after President Obama built his candidacy around a promise to change Washington’s partisan culture – this year the nominees had to be prompted into talking about it at all. Romney said he’d sit down with Democrats on day one. But Obama noted that Romney also wants to start rolling back the health care law.

So, Obama implied, Democrats would already be mad.

The arguments the two sides did put forward, in their limited time onstage, signaled sharply different theories of what voters want.

Romney and Ryan seemed to imagine the American electorate like a business, trying to hire a contractor.

In that view, voters would want to see a work plan first, even if details were left negotiable. Ryan seemed to mock Obama for not understanding that, and leaving out details of his plan to reduce the deficit.

“That’s what we get in this administration: speeches,” Ryan said. “But we’re not getting leadership.”

In the debates, the two Republicans did spend time talking about Romney’s business experience and generosity. Ryan, for instance, told a story about Romney helping members of his church, whose two sons had been left paralyzed by an auto accident.

“Mitt Romney’s a good man. He cares about 100 percent of Americans,” Ryan said.

But the two Republicans spent more time talking about their ideas to strengthen the military, and to pare back other parts of government.

In many cases, the two still left the details of these ideas fuzzy. Romney said he wanted replacement bills on health care and financial regulation, but spelled out only a few specifics. He also didn’t specify how he would cut tax breaks, to make sure that tax revenue doesn’t decline when overall rates are cut.

The Democrats had a different idea: Obama and Biden seemed to imagine the public like a football team, trying to hire a coach.

“Folks, follow your instincts on this one,” Biden said during his debate, talking specifically about Medicare.

Both Democrats dwelled on one specific policy idea: the proposed “Buffett Rule,” which would raise tax rates on some high earners.

But not many others. Obama lapsed into a familiar campaign-trail habit: phrasing his agenda in terms of questions, not answers. “How do we deal with our tax code? And how do we make sure that we are reducing spending in a responsible way?”

Biden also attacked Romney as untrustworthy, citing the secretly taped speech in which Romney said 47 percent of the population consider themselves “victims.”

So what would Biden and Obama do for those people?

Biden didn’t mention a specific bill. Instead, he described the noble – and highly intangible – goals that he and Obama shared.

“The president and I are not going to rest until that playing field is leveled, they, in fact, have a clear shot, and they have peace of mind,” Biden said.