Richard Carmona, the Democratic candidate for senator from Arizona, had a rough childhood in New York City. His Puerto Rican parents had drug and alcohol problems, and he was homeless for a time. He dropped out of high school and went to Vietnam, where he won two Purple Hearts and two Bronze Stars.

When Carmona came back, he put himself through college and became a police officer. He once rescued a man on a cliff by rappelling from a helicopter. Another time, he saved a woman from an assailant and then shot and killed the man when he fired at Carmona.

In his spare time at college, Carmona earned a medical degree. In fact, he served as surgeon general during George W. Bush’s presidency.

Carmona has yet to leap a tall building in a single bound, but Democrats here are counting on him to provide some political heroics: They’re hoping Carmona will not just take a Republican seat but also give President Obama the boost he needs to win Arizona, the one red state his campaign thinks can be turned blue this year.

“The perspective out here is if a group of consultants got together in a room and wanted to build a perfect candidate, we’d come out with Carmona,” said Bob Grossfeld, an Arizona Democratic strategist.

Barry Dill, another Democratic consultant in Arizona, said, “Him having a Hispanic surname, being Hispanic himself, speaking fluent Spanish — I think some of us Democrats are thinking that he may have more coattails for the president than the president may have for Dr. Carmona.”

Picking up a Senate seat and the state may be wishful thinking for Democrats. The biggest issue here — the state’s controversial law targeting illegal immigration, which the Obama administration has asked the Supreme Court to overturn — is very popular among Arizonans and has been a political boon to Republicans.

Obama’s approval rating in Arizona stands at about 40 percent, much lower than his standing nationally, according to numbers released by Gallup in January. And Bill Clinton is the only Democrat to have won here in more than half a century — and he barely did so on his second try, in 1996, with Ross Perot peeling off 8 percent of the vote.

“The fundamental problem with the national Democrats’ spin on Arizona is that it’s just that – spin,” said National Republican Senatorial Committee spokesman Brian Walsh.

“They thought they were going to take over the [state] Senate and the House two years ago,” said state Sen. Russell Pearce, sponsor of SB 1070, the anti-illegal-immigration bill. “We got the largest majority ever in the history of the state of Arizona in the Senate and the House. And you know what brought it there? SB 1070.

“So, it’s nice to have hope and dreams, you know, but it ain’t gonna happen,” he added.

At the moment, though, two recent independent polls show Obama and former Massachusetts governor Mitt Romney, the presumed Republican presidential nominee, in a dead heat in Arizona. Obama campaign manager Jim Messina argued during a conference call last week that the polls show that “there are even more pathways [to the presidency] than there were before.”

First lady Michelle Obama made a stop in Tucson on Monday, telling a crowd of hundreds that her husband will win the state because of supporters like them.

Dill, who served as deputy state director for Clinton’s 1996 reelection bid, said that the elements that produced that victory — support from 60 percent of independents, a sizable share of crossover Republican women and high Hispanic turnout — can be replicated this year.

Aiding Democrats among those three groups, those in the party argue, are the recent contraception debate, both nationally and within Arizona; the state’s burgeoning Latino population — particularly an increasingly involved Latino youth movement — and what Democrats argue is a backlash among voters against the state’s immigration law.

And then there is Carmona, who Democrats believe is perfectly positioned to capi­tal­ize. Arizona Democratic strategist Mario Diaz described the coattail effect he expects from him as like a bridal train — “It’s so long that everybody’s going to ride this tail,” he said. “And really, the Latino population is more motivated to flex its political muscle than I’ve seen it in my 26 years in Arizona.”

On a recent typically sunny afternoon, Carmona stopped by his newly opened Tucson campaign office to meet with volunteers. His voice was strained from laryngitis that he said he had picked up from talking so much on the campaign trail.

He spoke of the improbable paths his life has taken: His childhood in Harlem, growing up as the eldest son of Puerto Rican parents who “were good people, but they struggled with some of the substance and alcohol problems.”

At one point his family was homeless. At another, he lived with 11 others in his grandmother’s rent-subsidized apartment in a Bronx housing project.

At 17, he joined the Army and went to Vietnam. While he was there, his girlfriend at the time — now his wife, Diane — sent monthly packages and took care of a goldfish that the couple had won at Palisades Park before Carmona departed. As long as the goldfish was alive, she would say, Carmona would be, too.

What the couple later discovered after Carmona’s return was that the original goldfish had died long ago, and that Diane’s mother had made frequent trips to the pet shop for replacements.

After returning from Vietnam, Carmona earned a GED and attended Bronx Community College through an open-enrollment program for veterans — an opportunity he describes as “my own version of the Dream Act.” He went on to get his bachelor’s and medical degrees from the University of California at San Francisco, and later a master’s in public health from the University of Arizona.

He built dual careers in medicine and law enforcement, including work as a trauma surgeon and health-care administrator and as a deputy in the Pima County Sheriff’s Department. He was named surgeon general in 2002 and served one term. At a 2007 congressional hearing, he strongly criticized the Bush administration for placing political considerations ahead of scientific ones.

“You know, having walked in those shoes of being hungry and being homeless — the indignities of not getting health care, or waiting in the public hospital, hoping somebody will care for you; going to sleep with a toothache because you can’t go to the dentist,” he said. “I think it was, in retrospect, almost a gift of experience to me that sensitized me to the complexity of the world that we inherit today.”

Republicans tried to recruit Carmona to challenge both Rep. Gabrielle Giffords (D) and then-Gov. Janet Napolitano (D) in 2006, but he declined. This time around, it was Obama who did the recruiting, calling Carmona in September to encourage him to run.

Carmona, who was registered as an independent until November, is unopposed on the Democratic side after former state party chairman Don Bivens dropped out of the race in March.

His likely GOP opponent is Rep. Jeff Flake, a six-term member of Congress whose strategy suggests that he will run against both Carmona and Obama.

“For Richard Carmona, having the president’s support — that’s nothing I would want to tout very loudly,” Flake said in an interview after a recent town hall meeting in Fountain Hills, a suburb about 30 miles outside Phoenix.

He added with a laugh: “I would welcome the president to come here and campaign with my opponent.”

Carmona played down his relationship with Obama, whom he first met briefly in 2005 when they both appeared on “Larry King Live” together nine days after Hurricane Katrina reached its peak.

“Here’s my thought: My focus really is about my campaign,” Carmona said. “The president has to run his campaign as he sees fit, and whatever he thinks is correct. I have to run my campaign that way.”

Sitting on a couch in the darkened lobby of the community center after his town hall meeting, Flake discounted the attention Arizona will attract in the presidential election. The stakes for the Senate, he said, will be higher. In its 100-year history, there have been fewer senators from Arizona than presidents.

“In 100 years, we’ve only had 10 U.S. senators,” Flake said. Five of those were Democrats and five were Republicans. “They tend to serve a long time,” he added, “so we’ve got to choose carefully.”