President Bush made a last-minute dash into Virginia’s bruising governor’s race, hoping to give a bounce to the Republican candidate in one of several contests being closely monitored for evidence of how the GOP’s recent struggles are influencing voters.

Bush lent his support Monday to Jerry Kilgore, exhorting die-hard conservatives to help turn out voters in the former attorney general’s race against Democratic Lt. Gov. Tim Kaine.

“The thing I like about this fellow is he grew up on a farm,” Bush said in a brief stop on his return from a South American trade mission. “He doesn’t have a lot of fancy airs.”

At a campaign event for Kaine, the Democratic incumbent, Gov. Mark R. Warner, welcomed the president’s arrival. Bush, even in reliably Republican Virginia, suffers job-approval ratings of around 40 percent.

“If they want to compare how things are going in Washington versus how things are going in Virginia, I’ll take that comparison every day of the week,” Warner said.

The gubernatorial races in Virginia and New Jersey — the biggest contests in this off-year election season — have broken spending records in both states, gotten progressively nasty and yet remain virtually tied.

In New Jersey, U.S. Sen. Jon Corzine campaigned with fellow Democrat U.S. Sen. Frank Lautenberg while Republican candidate Doug Forrester enlisted New York Gov. George Pataki for a frantic final day of campaigning.

In other contests today, the cities of New York, Detroit, Houston, Boston, San Diego and Atlanta have mayoral races. Seven states are considering ballot issues, including four proposals backed by California Gov. Arnold Schwarzenegger that are trailing in the polls.

Schwarzenegger’s initiatives would cap state spending and give him more power to cut budgets, rein in public employee unions, and take away legislators’ power to redistrict.

“I’m never going to give up because I have the people power,” Schwarzenegger told cheering supporters at a retirement community in suburban Sacramento. But in a widely played radio ad, Schwarzenegger nemesis Warren Beatty tells voters, “Don’t give him more power.”

In New York, Republican Mayor Michael Bloomberg held onto a clear lead against Democratic underdog Fernando Ferrer, who campaigned with the Rev. Al Sharpton and Sen. Barack Obama of Illinois.

Ferrer, the former Bronx borough president, has spent only about an eighth of the more than $66 million that the billionaire mayor has funneled toward winning a second term.

In Boston, Mayor Thomas M. Menino hopes to set a record for the longest serving mayor in city history, while challenger Maura Hennigan wants to become Boston’s first elected female mayor.

Detroit Mayor Kwame Kilpatrick campaigned for another term, but is fending off allegations of misspending. Kilpatrick blames the fiscal problems on his predecessor, Dennis Archer, for whom challenger Freman Hendrix worked.

Allegations of ballot improprieties also have surfaced. A judge has ordered Detroit election officials to oversee absentee voting after finding problems with the way the city clerk organized the effort.

Voters in Texas are being asked to decide whether a state constitutional ban should be placed on same-sex marriage. And in Maine, a referendum seeks to repeal the state’s anti-discrimination law.

In San Diego, Donna Frye, a surf-shop owner and Democrat, was staging an uphill battle against Republican Jerry Sanders, who enjoys strong backing from the city’s business establishment.

Four constitutional amendments in Ohio would expand voting by mail, limit campaign contributions and create bipartisan boards to draw districts and oversee elections. The amendments were proposed by Democratic-leaning groups in the state they blame for costing them the White House last year.

Recent polls show the gubernatorial race in Virginia — estimated to have cost a record $42 million — has tightened. Kaine got 45 percent of voters, and Kilgore had 44 percent in a survey released Friday by the Mason-Dixon Polling & Research. The gap was well within the poll’s error margin of 4 percentage points.

The race in New Jersey also was tight. A Quinnipiac University poll released Monday showed Corzine at 52 percent to Forrester’s 45 percent. The sampling error margin was plus or minus 3.5 percentage points.

To date, Corzine and Forrester have spent a combined $70 million on the priciest campaign in state history, much of it their own money going to TV and radio advertising criticizing each other.

“All I’ve seen is negative campaigning,” said Nick Russo, a New Jersey businessman. “I can see why people get frustrated with that. You get tired of hearing this. It just turns you off.”

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Associated Press writers Bob Lewis in Richmond, Va., Angela Delli Santi in Westfield, N.J., and Sara Kugler in New York City contributed to this report.