Carlos F. Lazo, an American military medic on 15 days' leave from Iraq, wanted to see his teenage sons in Cuba. He flew to Miami, only to be told that new Bush administration rules designed to punish Cuba made it impossible.

"I just wanted to see my children for one day. In the next eight months in Iraq, who knows what could happen?" Lazo said yesterday. "I got very mad. I am not voting for George Bush this year."

Lazo's anger is at the heart of a charged debate over Cuba policy and Florida politics that could prove pivotal in the Nov. 2 election. In a gamble designed in part to capitalize, Democratic challenger John F. Kerry is taking a position different from that of hard-line Cuban exiles courted most often by both parties and considered the Cuban Americans most likely to vote.

Opponents of the measures include the Cuban American National Foundation, a no-nonsense anti-Castro organization at the forefront of U.S. policy toward Cuba for two decades. The group issued a statement saying the administration's new measures "created a greater divide" among Cuban Americans.

President Bush chose Wednesday, barely four months before the election, to impose some of the most restrictive measures ever on Americans' travel to Cuba and on Cuban Americans' practice of sending money to relatives on the island.

The goal is to squeeze Cuban President Fidel Castro by denying hard currency to his wheezing economy. But the first to cry out have been Cuban Americans, who now can visit only once every three years, with no exceptions. Money can be sent only to immediate family members.

"We're not waiting for the day of Cuban freedom, we are working for the day of Cuban freedom," Bush said May 6 in accepting the recommendations of a government commission headed by Secretary of State Colin L. Powell. A Powell adviser called the 423-page document a "decisive and integrated strategy."

Many critics and supporters alike viewed the policy as a play for Cuban American voters, whose greatest concentration is in Florida, a state that gave Bush a 537-vote victory margin and the White House in 2000. But Democrats see an opening in a combination of changing demographics and the Bush administration's policy.

"There's going to be the kind of recoil that they haven't really seen before," predicted Dan Gelber, a Democratic member of the Florida House. Kerry supports an economic embargo against Cuba, but favors lifting travel restrictions and increasing remittances.

"If the Democrats want to make the new Cuba travel regulations a referendum on President Bush's candidacy in November, all I can say is bring it on," said state Rep. David Rivera, a Republican who criticized Bush last year for being too soft.

"The initiative will serve to galvanize and motivate Cuban American voters to turn out in support of the president," Rivera said. "The people who vote are older people, and the people who are most supportive of these measures are the hard-core, historic exiles."

Miami pollster Sergio Bendixen is among the specialists attempting to test that tried-and-true view. He estimates about 250,000 voters in Miami-Dade County fit Rivera's designation of "historic exiles," those who arrived between Castro's triumph in 1959 and the late 1970s.

"It's two theories," Bendixen said. "We won't know who's right until Election Day."

Conducting a poll last month for the centrist New Democratic Network, he found that 89 percent of that cohort favored Bush, 8 percent chose Kerry and 3 percent were undecided. The results from two other groups he polled were quite different.

A second group of Miami-Dade Cuban Americans, numbering about 75,000, is composed of men and women who fled the island in the 1980s and '90s. This group has closer ties to Cuba and more relatives back home.

"They like to go back for weddings, for when someone gets sick, for the birthdays, for the graduations. They send remittances," Bendixen said. "They would never be supportive of Fidel Castro in any way, but they're not obsessed with his removal."

Bendixen's poll suggested that 40 percent of that group supported Kerry and 28 percent backed Bush. Thirty-one percent were undecided.

A third group contains about 50,000 Cuban American voters, Bendixen estimates. As American-born children of Cubans who left the island, the segment has for the first time become large enough to poll during this election cycle.

"We are finding that Cuba policy is of no special interest to them," Bendixen said. Respondents in this group backed Kerry over Bush by 58 percent to 32 percent, with 10 percent undecided.

Overall, Bendixen's poll found that 69 percent of Cuban Americans favored Bush to 21 percent for Kerry, with 10 percent undecided. If accurate, that would be a fat Republican margin -- but a significant drop for Bush, who received an estimated 80 to 85 percent of the Cuban American vote in Miami-Dade in 2000.

A Florida International University poll of Cuban American registered voters in Miami-Dade and neighboring Broward County found earlier this year that about 60 percent supported Bush, while about 25 percent said they remained undecided. The poll was conducted for the South Florida Sun-Sentinel and NBC-6.

Lazo, a counselor for the developmentally disabled, left Cuba on a raft 12 years ago. After a stay in Miami, he moved to a town north of Seattle. He is now a Washington National Guard medic.

Deployed to Iraq, he followed Cuba policy over the Internet. On leave, he flew to Miami in hopes of visiting his sons before new licenses were required.

"Nobody knows whether I'm going to give my life, but at the same time, the president doesn't let me go to Cuba to see my children," he said. "I think that's not fair."