There are two ways to go about eating a pie. You can sit down with a fork and settle in for a struggle. Or you can cut it into slices and revisit it over several sittings.

That's where congressional leaders are now on attempts for a major overhaul of immigration laws.

Should they wait for the comprehensive package, gambling that some heretofore elusive breakthrough will land on their plates? Or should they slice off what they can, when they can?

"That's the question everyone is asking right now," said Wendy Sefsaf, a spokeswoman for the Washington, D.C.-based Immigration Policy Center, which advocates a comprehensive approach.

So far, the Obama administration and Democratic leaders are holding out for one big package. The president acknowledged to Gov. Jan Brewer Thursday that there is frustration about the broken immigration system, but he reiterated his belief that security measures alone aren't a solution.

The president, who has a reputation as pie aficionado around the capital, said he wants the whole thing when it comes to immigration - better security, penalties for hiring illegal workers, fines and back taxes paid by those here illegally, and a requirement that those who stay must learn English.

U.S. Rep. Raúl Grijalva has likewise been holding out for comprehensive change. But given the tenor of the times, he acknowledges being tempted, though not yet persuaded, to grab a couple of quick slices.

He's not alone. Discussions are under way about breaking out more manageable pieces - such as an agricultural-worker program or one that allows undocumented students to become permanent residents if they came to the country as children - as political down payments for a larger package.

Which way to go, and when, hangs on a number of political variables: Who wants to brave such a hot debate right before midterm elections, which are tough on the party in power anyway? Did health care suck up too much political capital for now?

Then there's the political-payback question. Obama's decision to send National Guard troops to the border left his liberal base woofing for a bone, if the secure-borders folks were going to get red meat.

"It's misdirected symbolism," Grijalva said of Obama's move, which he dubbed "a big win" for U.S. Sen. John McCain.

"It's good political cover for some people, but the people we really worry about - the drug smugglers, the people smugglers - they don't care about the National Guard or about 1070," said Grijalva, referring to the newly passed Arizona immigration law. Grijalva, a Democrat, represents the Arizona border area from Tucson westward.

"Now that we've had this political gesture, I would hope the people who asked him to do this will join with those of us who had to watch it happen and urge him to do comprehensive immigration reform," he said.

And until that happens, Grijalva acknowledged that there is increasing pressure to tackle some of the other pieces. "The concern is that if you do it piecemeal and get to the easier parts first, the difficult parts will never get done," he said. As pieces come out, more interest groups peel away from supporting the package.

Still, Grijalva said, if the Dream Act benefiting immigrant students came up, "it would be difficult not to support that."

Sefsaf, of the Immigration Policy Center, said there's another risk as well.

"You don't want to put it out there and lose. If you put 'Dream' out and lose and you put out ag jobs and lose, then what does that mean for comprehensive reform?" she asked. "No one wants a kamikaze mission."

On the other side, the experience of the recent health-care overhaul has some politicians skittish. The bigger the solution, the bigger the confusion and the bigger the critic pool. In retrospect, some later said they'd wished health care had been broken into more bite-size pieces.

John Garcia, a University of Arizona political science professor, said Congress should consider taking what it can get. "People pushing for comprehensive reform are getting really frustrated because of the logjam and because there's really nothing on the agenda," he said.

"If you could get parts like the Dream Act or the agricultural provisions, you could generate some momentum," Garcia said. "It would raise expectations." Waiting for a bigger package, he said, "can be seen as a push - or it can be an excuse."

McCain, who supported comprehensive immigration legislation in the past, has repeated the secure-the-border-first mantra at town-hall events across the state. U.S. Rep. Gabrielle Giffords, a Democrat who represents Southeastern Arizona is more aligned with McCain than with Grijalva on that point.

"The way I see things, before we move forward with even smaller pieces of an immigration solution, we have to focus on border security first," said Giffords, who unlike Grijalva was pleased with Obama's National Guard deployment. She represents the border area from Tucson eastward.

Recent news reports saying that border violence is down "completely missed the point," Giffords said. With 240,000 apprehensions last year in the Tucson Sector alone, with drug seizures up and with kidnapping becoming a growing problem, voters are understandably frustrated, especially border ranchers.

The solution is complex, she said, but it includes better enforcement of laws already on the books, changing the employee-verification system and building up resources in the rural areas along the border.

William Gheen, of the anti-amnesty Americans for Legal Immigration, said he doesn't care whether legislation comes in little pieces or in one fell swoop.

"We're not advocating either of those approaches," Gheen said. "The reforms are unnecessary. We don't have a problem created by a lack of reform. The problem is that our border laws aren't being enforced."

Contact reporter Rhonda Bodfield at 573-4243 or