COLUMBUS — The way Democrats figure it, they borrowed about 500,000 voters in bellwether Ohio last year and ended more than a decade of statewide political frustration. Now they seek a more durable relationship in time for the 2008 presidential election.

Their salesman of choice?

That would be Gov. Ted Strickland, off to a fast start as the state’s first Democratic chief executive in 16 years, and the face of an attempt to remake the party in his own soothing, centrist image.

As governor, he said in an interview in his statehouse office, ‘‘we’ve tried to avoid being overly partisan.’’ As party builder, he said he wants to focus on ‘‘what I call the kitchen table issues … the basic issues that are important to a family’s quality of life.’’

Strickland’s first budget passed with only one dissenting vote in the Republican-controlled legislature. It included a property tax cut for seniors and the disabled as well as more money for higher education. It also provided health insurance for children living in families with up to about $62,000 in income — a bipartisan accomplishment that stands in contrast to the veto struggle now unfolding in Washington over the same issue.

No Republican has ever won the White House without carrying Ohio, and President Bush sealed his second term with a statewide victory of 118,601 votes. Two years later, an estimated 563,000 Ohioans who supported Bush backed Strickland for governor, and 442,000 of the president’s voters helped Sherrod Brown topple Republican Sen. Mike DeWine.

Already, the party has sent out thousands of pieces of mail bearing Strickand’s picture, urging likely Democratic voters to seek absentee ballots for 2007 municipal elections.

Mail will go out to the presumed Bush-Strickland voters over the winter, a reminder to them, party officials say, that they sought change at the polls and got it.

‘‘The governor is re-establishing the state Democratic Party,’’ conceded Rep. Pat Tiberi, a former leader of the Legislature elected to Congress in 2000. Referring to former Republican Gov. Bob Taft’s plunge from political grace — the state Supreme Court reprimanded him over ethics violations — Tiberi pointedly noted that a governor’s popularity can erode quickly.

Besides, he said, ‘‘The unanswered question on the Democratic side is, ‘Does Ted Strickland’s moderate attraction for independents as a pro-gun minister from southeast Ohio flip over to the presidential candidate?’’

A few miles north of the state Capitol, in the suburb of Worthington, the voters Democrats covet are in plentiful supply, their future political decisions unmade.

Jenny James, a 30-year-old event planner, hurries into Flowers On High. ‘‘I did vote for Strickland,’’ she says, adding she doesn’t recall having heard much about what he’s done since taking office.

‘‘I consider myself a conservative, but I didn’t vote for Bush’’ in 2004, she said. Looking ahead, she says she likes Democratic presidential front-runner Hillary Rodham Clinton ‘‘but not just because she’s a woman.’’ In the next breath, though, she says she also likes former New York Mayor Rudy Giuliani, leader in nationwide polls for the Republican nomination.

Kim Youse, 46, voted for Bush as the ‘‘best of two evils,’’ and now says Strickland ‘‘is doing OK. I don’t think he’s doing outstanding.’’ She struggles with the war in Iraq. ‘‘I think there need to be some troops coming home,’’ she said, but ‘‘I don’t think all the troops should come home.’’

As for 2008, ‘‘I will vote, but I haven’t decided yet. I keep waiting for somebody.’’

Ohio’s historic status as a must-win state for Republicans, combined with poll ratings of over 60 percent for Strickland, have Republicans wondering aloud whether he might be a potential vice presidential running mate on the Democratic ticket.

In another breath, though, they say their loss of a Senate seat, House seat, the gubernatorial election and three other statewide offices in 2006 was unlikely to signal a long-term trend.

Last year was ‘‘less about the party and more about nonperformance and personal conduct,’’ says Kevin DeWine, leader of Republicans in the state House and in line to become the next state party chairman.

Taft was deeply unpopular for having raised taxes as well as for ethics woes, and the war in Iraq was a drag on Republicans nationally. Add to that Rep. Bob Ney’s conviction on corruption charges, a homegrown example of congressional wrongdoing.

DeWine said Republican legislators as well as Strickland deserve credit for the budget, and the GOP will have ample time to sharpen its differences with the governor on issues such as private school vouchers.

Democrats aren’t waiting.

Strickland recalled a conversation shortly after his election with David Wilhelm, his friend and a former chairman of the Democratic Party under President Clinton. ‘‘David said to me, ’we borrowed a lot of voters in ’06 but we don’t own them.’’’

Democrats believe they have determined which of Ohio’s counties those voters reside in. Through sophisticated research they intend to try to begin contacting them by mail and phone in the coming months.

In the first visible stirrings of the effort to strengthen the party, Democrats dispatched organizers into areas that normally go unattended until shortly before statewide elections.

The party also recently contacted thousands of voters urging them to apply for absentee ballots for this fall’s municipal elections. The mailers bore a picture of the governor, with an upbeat message: ‘‘While we’ve made progress, there’s more to do,’’ said one. ‘‘I need partners in communities like yours to help bring new opportunities to Ohio. That’s why I need your help to elect strong Democratic leaders all across Ohio this year.’’

Lack of a reply prompts a second mailing, a Strickland appeal slightly more pointed than the first. ‘‘The fastest way to help me Turn Around Ohio is to vote by mail to elect good Democrats,’’ it says. ‘‘If you haven’t already, please send in your application today.’’

Municipal balloting aside, the Democratic political wish list for Ohio includes capturing control of one house of the Legislature in 2008 and challenging for four or five congressional seats now in Republican hands, including two where veteran GOP lawmakers are retiring.

Re-electing Strickland and other statewide officers in 2010 is next on the agenda, which would in turn give Democrats a majority on the commission that will oversee redistricting of the state’s legislative districts in 2011.

But first there’s the matter of the White House.