Republicans running for governor of Illinois are not supposed to be struggling against the odds. It has been 30 years since a Democrat was elected to the top job in Springfield, but this year, every poll for months has showed Democrat Rod R. Blagojevich, a relatively little-known junior House member from Chicago, running ahead of Republican Jim Ryan.

Indeed, few Republicans face as many vexations as Ryan does. He has had to endure the confusion of his name with that of the retiring GOP governor, George H. Ryan, who has been enmeshed in scandal. At the final debate of the campaign, held here last week, reporters pressed him about the drivers' license bribery cases that occurred when George Ryan was secretary of state -- well before Jim Ryan was first elected state attorney general.

The circumstances in Illinois are unique, but across the country Republicans are facing so many problems that Democrats could emerge with a majority of governors for the first time since 1994. A combination of retiring incumbents, slumping revenues and, in many states, strong Democratic challengers has put the GOP's strength in the state houses in serious jeopardy, particularly in the industrial Midwest. The likelihood of a significant power shift is far greater in the 36 gubernatorial elections than in the House or Senate contests.

While overshadowed by the close battle for Congress, the gubernatorial races could turn out to be of greater political importance. Four of the last five presidents have come from the ranks of governors. George W. Bush's path from the Texas governorship to the White House was smoothed by other Republican governors -- 28 of them at the time -- who mobilized their contributors and their campaign organizations on his behalf.

Having his brother Jeb in the Florida governorship was vital to Bush in the recount battle that ultimately gave him the presidency, and keeping Florida Republican was the top priority for White House operatives -- at least until recent polls indicated that the upset bid of Democrat Bill McBride appeared to be falling short.

Scott Reed, a Republican consultant who managed Robert J. Dole's 1996 presidential campaign, said the likely power shift among governors has large implications. "For the last 10 years, Republican governors have been the backbone of the party, the incubator of ideas, the financial base and the key players in presidential campaigns," Reed said. "It looks like there will be a reversal this year -- especially in the Midwest. If California is out of reach [for Bush in 2004], the Midwest will be critical, and it will be tougher to win with Democratic governors setting the agendas in those states."

Illinois may offer the worst-case scenario for Republicans, but around the country, so many governors were first elected in the banner GOP year of 1994 and now face term limits that Democrats find themselves with a wealth of opportunities. Republicans are defending 23 governorships, the Democrats 11. Two are held by retiring independents. Twelve Republican states are open (without incumbents running), while Democrats have only six open seats to defend.

Wins last year in Virginia and New Jersey upped the Democratic total to 21 governorships and a net gain of five governorships -- for a majority -- appears to be well within their reach.

Among the other states where Democrats are favored are Michigan, Pennsylvania and New Mexico, all now in the GOP column, and Maine, where independent Gov. Angus S. King Jr. is stepping down after two terms.

In the private scorecards of both parties, Democrats are highly competitive also in Arizona, Kansas, Massachusetts, Rhode Island, Tennessee, Wisconsin and Wyoming, all of which have GOP governors, and Minnesota, where independent Jesse Ventura is retiring. Against those dozen Democratic opportunities, Republicans have a shot at replacing Democrats in seven states: Alabama, Alaska, Hawaii, Maryland, Oregon, South Carolina and Vermont.

A few governors in each party appear to be strong enough to ride to reelection despite the revenue slump that has opened budget holes in the vast majority of states across the country.

Among the safe or favored Republicans are Mike Huckabee of Arkansas, Bill Owens of Colorado, John G. Rowland of Connecticut, Jeb Bush of Florida, Dirk Kempthorne of Idaho, Mike Johanns of Nebraska, Kenny C. Guinn of Nevada, George E. Pataki of New York, Bob Taft of Ohio and Rick Perry of Texas.

The Democrats who are leading their races include Gray Davis of California, Roy E. Barnes of Georgia and Tom Vilsack of Iowa.

Here in Illinois, Republicans have not given up on salvaging the governorship, but admit they are facing tough odds. Multiple indictments of officials in the secretary of state's office when George Ryan was its head have brought the issue of corruption in Springfield, the state capital, to a head. Blagojevich has criticized Jim Ryan repeatedly for "not lifting a finger" to investigate the bribery charges after becoming attorney general eight years ago. Jim Ryan's defense is that federal prosecutors were on the case and he could only have gotten in their way.

If the current governor's troubles were not enough, Jim Ryan also endured a tough three-way primary, in which a moderate woman and a hard-right conservative took turns assailing him. Meantime, Blagojevich (pronounced Bluh-goya-vich) dispatched a credible but underfinanced opponent, former Chicago public school chief Paul G. Vallas, by rolling up a vote in normally Republican downstate Illinois.

Republicans have tried to turn the corruption issue against Blagojevich, the son-in-law of a powerful Chicago alderman and ward boss, by identifying convicted criminals who were part of that ward organization. They also have assailed the lawmaker for missing votes during the campaign. An endorsement of Ryan by the Chicago Tribune on Sunday may help with suburban independents. But it remains an uphill struggle.

In the debate, Ryan acknowledged, "People are angry. People want change," then went on to argue that it requires "more than a change of names or political parties." As an 18-year prosecutor, "never tainted by corruption," he said, "I am the one to end the sleaze."

But as a Republican strategist conceded, "That's a more complicated argument to make" than Blagojevich's simple declaration: "You can vote for the status quo or you can vote for change. I think Illinois is ready for change."