Washington ? The story that Kansas Gov. Kathleen Sebelius was telling this week about the struggle over school financing that has preoccupied her time in office reveals something very significant about the changing mood of the public – a change that could alter the dynamics of the next presidential race.

Sebelius, visiting Washington for the winter meeting of the National Governors Assn., described how a seven-year-old impasse over court-ordered increases in Kansas’ education funding finally has moved toward resolution.

After the Republican-controlled Legislature ended its regular session in 2005 deadlocked over the state Supreme Court funding mandate, Sebelius, a Democrat, called the lawmakers into a special summer session. They cobbled together a $148-million fix, and when the court said that was still inadequate, something dramatic happened.

“The legislative leaders of both parties said, ‘We have to have a plan, and we want to be at the table when it’s hammered out,”‘ Sebelius said. The result: In February, a new, bipartisan proposal for a three-year boost in school budgets began working its way through the Legislature.

As Associated Press reporter John Milburn wrote, “Unlike previous years, when school finance plans were hatched by dissident Republicans and a handful of Democrats and sometimes tended to reflect narrow interests, legislative leaders put their heads together with Gov. Kathleen Sebelius from the get-go to find a solution.”

Sebelius says that the real pressure was not just the court ruling but public opinion, demanding that “we have to work together, and it can’t be just Republican or Democratic.”

By contrast, she said, “when people look at Washington, D.C., they are dismayed. They see a sea of partisanship, but no results.”

That is emphatically the view of almost all the dozen governors of both parties I interviewed during the NGA meeting, including two who have been among the most active in testing the 2008 presidential waters.

Mitt Romney, the Republican governor of Massachusetts, is in a mirror-image situation to Sebelius, working with an overwhelmingly Democratic Legislature. “At the state level,” he said, “when the election is over, there’s a meeting of minds and a readiness to find solutions. When we saw the Katrina refugees were coming, we passed a $25 million emergency appropriation in one day.”

While Romney’s ambitious health reform – aimed at insuring every resident, without having to raise taxes – is still hung up in the Legislature, he said “there is not the same level of bitterness you see in Washington – the gotcha mentality.”

Romney said he recognizes that some Republicans were as antagonistic toward President Clinton as some Democrats are now toward President Bush. But on the hustings, he said, people hunger for a return to the spirit of the Reagan years, when Tip O’Neill and Reagan quarreled over policy but then shared stories and trust.

Tom Vilsack, the Democratic governor of Iowa, said he finds people “genuinely concerned about the lack of action in Washington. They think their state is going in the right direction but the country is not. Governors of both parties routinely reach across the aisle, and people love to see that.” Vilsack, who faces a Republican House and an evenly divided state Senate, added, “The (public) attitude toward Washington is a pox on both your houses.”

What all of them are describing helps explain why Democratic governors are flourishing politically in “red states” such as Arizona, Montana and Wyoming, and why Republican governors are favored for re-election in such “blue” states as Vermont, Connecticut and Minnesota.

It also suggests why there may be a special burden on presidential candidates whose experience and credentials have been forged largely in the partisan warfare of Washington, D.C.

In 2000, Sen. John McCain largely avoided the label of extreme partisanship because of his reputation as an independent thinker. But he still lost the Republican nomination to Bush, who campaigned as someone whose record in Texas showed him to be “a uniter and not a divider.”

Sen. Evan Bayh of Indiana, one of the Democratic contenders for 2008, has obviously picked up these vibes. In interviews and stump speeches, he dwells much more on his experiences as governor for eight years than on his current membership on the Senate Intelligence Committee.

But what about Hillary Rodham Clinton? She leads all the early polls for the Democratic nomination. But can she avoid being seen simply as a battle-scarred veteran of the partisan Washington wars? Is there anything in her record that speaks to the hunger for consensus?