OODBURN, Ore., April 5 — Ever since she became an American citizen 20 years ago, Ana Maria Guerrero has voted for Democrats. Even so, Mrs. Guerrero, 46, a cannery worker, is the kind of Hispanic voter that politicians of both parties see as a golden prize: one whose party loyalties are up for grabs.

"I'd vote for a Republican if that person worked to make a big change for Latinos," Mrs. Guerrero said at a farm workers' union hall here, speaking in Spanish of her concerns for better health care and education.

And as the number of Latinos swells, people like Mrs. Guerrero, who said she would consider casting a ballot for a Republican who "showed respect for Latinos," are indeed commanding the respect of political strategists of all stripes.

The nation's Hispanic population grew by nearly 60 percent in the last decade, to 35.3 million, roughly equaling blacks as the country's largest minority. As Hispanics strive to translate their numbers into the kind of political influence that blacks have achieved, the battle is on among Democrats and Republicans to court this still largely untapped and disparate voting group.

Hispanics have long held political sway in big immigrant-rich states like California, Florida and Texas. But data from the 2000 census show that Latinos are gaining a foothold in plenty of unlikely places, like Iowa, North Carolina and here in Oregon, where the Hispanic population more than doubled in the 1990's, to 275,000 people, or 8 percent of the state.

Oregon's shifting demographics are forcing politicians like Senator Gordon H. Smith, a Republican who faces a potentially tough re-election fight next year against the Democratic governor, John Kitzhaber, to devise campaign strategies aimed for the first time at Latinos, many of whom are deeply skeptical of a party they view as anti-immigrant.

The stakes are especially high for Republicans like Mr. Smith. Of the estimated 55,000 Hispanics registered to vote in Oregon, the vast majority are Democrats. In last fall's presidential race, Vice President Al Gore defeated Gov. George W. Bush by only 6,700 votes out of 1.5 million cast. Pollsters from both parties said Hispanics were probably decisive in swinging the state's seven electoral votes to Mr. Gore.

"The machinery of how to go after the Hispanic vote in 2002 is in its infancy," said Kurt Pfotenhauer, Mr. Smith's chief of staff. "What's important is what we do over the next 18 months to focus on getting this growing population to come to the polls and come to the polls for our candidate."

It is perhaps no surprise that Mr. Smith has championed a new guest- worker program that could lead to legal residency for millions of undocumented workers nationwide. He has sponsored legislation to provide federal aid to combat high school dropout rates, a critical problem among Hispanics. And on Tuesday, Mr. Smith will visit a health clinic for migrant workers outside Portland to promote a plan to expand health care for the uninsured, including many working-class Hispanics.

"I know the farm community and farm workers in very personal terms, and have watched how our laws have created this subculture that lives in the shadows," said Mr. Smith, who made his millions in frozen foods packaging.

Similar campaigns to win over Latinos are revving up across the country, on school boards and in legislatures, in Congressional races and in war councils in the White House.

Mr. Bush's strategists are already planning to build on the Spanish- language outreach program that helped him capture 31 percent to 35 percent of the Latino vote last year, according to various polls, the best showing for a Republican since Ronald Reagan in 1984.

But many in Republican circles express worry. Matthew Dowd, director of polling and media planning for the Bush campaign, has warned the White House and Congressional Republicans that if Mr. Bush were to win the same percentage of minority voters in 2004 as he did last year, he would lose by three million votes.

With that bleak forecast, Mr. Dowd, now a senior consultant for the Republican National Committee, has told Republican aides that Mr. Bush must increase his share of the black vote to 15 percent from 9 percent last year; the Hispanic share needs to rise to about 40 percent.

Earlier this year, Karl Rove, the president's senior political adviser, echoed the theme, telling reporters that capturing a bigger share of Hispanic voters "was our mission and our goal" and warning Republicans that that goal would "require all of us in every way and every day working to get that done."

Even so, political analysts caution against overstating the immediate impact of the Hispanic vote. About a third of the country's Latinos are under 18, and many newly arrived Hispanics are not yet citizens. In last year's presidential race, their influence was negligible because Latino voters are concentrated in states that offer the most electoral votes, like California, New York and Texas, and those states were solidly aligned with Mr. Bush or Mr. Gore. The Midwestern battleground states had far fewer Hispanics.

The nation's Hispanic and black populations are now roughly equal, but blacks hold 39 seats in the House; Hispanics hold 21 seats. To strengthen their representation, the Congressional Hispanic Caucus has set up a political action committee to identify, recruit and raise $2 million to $4 million for Hispanic candidates.

Redistricting could also create opportunities for Hispanics. The surprising surge of Latinos could turn Republican strongholds like Florida, Arizona, New Mexico and Colorado into swing states. Texas may soon join California as the second big state in which non-Hispanic whites are no longer a majority, and Democrats there are hoping to capitalize on this trend, possibly running a multimillionaire Hispanic businessman, Tony Sanchez, for governor.

More than 80 percent of Latinos in Congress and in state legislatures are Democrats, but that does not guarantee that new immigrants will align themselves with that party.

"Latinos are conservative on abortion, but very progressive on health care and gun control," said Harry P. Pachon, president of the Tomas Rivera Policy Institute, a research organization in Claremont, Calif.

Indeed, many Republicans are pinning hopes on Latino conservatism to help Mr. Bush overcome Democratic voter registration drives to win Hispanic support in 2002 and 2004.

"Democrats have won the first skirmishes, but it's a long battle and Republicans are bringing in the big bazookas," said Representative Thomas M. Davis III of Virginia, who heads the House Republican re-election committee. "There's no question the Republicans need a greater share of Hispanic voters to stay in the majority."

Here in Oregon, Democrats slightly outnumber Republicans, and nearly a quarter of registered voters are independents. Latinos' political visibility is slight. There is only one Hispanic in the 30-member State Senate, Susan Castillo, a Democrat from Eugene, and none in the 60- member State House.

There is a sprinkling of Latinos through county and local offices, including Serena Cruz, the first Mexican-American on the Multnomah County Commission, a five-member board that governs Oregon's largest county, which includes Portland.

Republicans here express confidence that their policies and values will attract Latinos despite registration that runs 9-to-1 for Democrats.

"The Hispanic population in Oregon is up for grabs," said Dan Lavey, a Republican political strategist who was the Bush campaign coordinator in Oregon. "The party and candidates who get there first, most often and with sincerity will have greater long-term success."

Republicans are counting on people like Enedelia Hernandez Schofield, 42, the daughter of migrant workers and principal of Echo Shaw Elementary School in Cornelius, outside Portland. Ms. Schofield was a Democrat who switched parties after studying Mr. Bush's education policy. "It agreed with what we were doing at this school," she said.

But Latinos here in Marion County, a farming community in the Willamette Valley 30 miles south of Portland, are divided. In the last decade, Woodburn became the largest Oregon city where Latinos are a majority (just over half of its 20,100 people, up 139 percent in a decade).

Rigo Mora, 38, whose clothing store on Front Street in Woodburn reverberates with Mexican band music, said the choice of parties was easy for him. "Republicans are doing a better job on taxes," he said.

But at a time when Republicans in the State Senate are pushing to abolish bilingual education, many Hispanics here cannot fathom the notion of voting for them, even moderate Republicans like Senator Smith.

Ana Maria Guerrero's husband, Hector, 46, a board member of Voz Hispana, a Latino voter participation group, shook his head when asked if he could ever vote Republican, saying, "Republicans seem bent on cutting all our programs."