Gov. Janet Napolitano and state Republican leaders clashed Wednesday over plans to send National Guard troops to the border, offering proposals that both sides concede are unlikely to fix the state's illegal-immigration problem.

Critics questioned the maneuvering, saying it reduced one of the most crucial issues facing Arizona to pure politics.

Early Wednesday, the governor issued an executive order to send Guard troops to the border to help with vehicle inspections and otherwise support the U.S. Border Patrol as soon as money becomes available. She did not specify how many troops would go or how much it would cost.

The Legislature then signed off on a different plan requiring the Guard to be stationed at the border at a cost to the state of $10 million, enough to pay for 100 soldiers for 311 days.

The governor called the measure unconstitutional because it usurps her authority to command the National Guard. "There is one commander in chief, not 90," she said.

Republicans countered by defending their measure. But amid the political back-and-forth, some questioned what impact 100 National Guard troops, regardless of how provided, could have in terms of securing a remote 389-mile border of Arizona desert and canyons.

"Trust me. They're not going to be able to handle it," said Robert Murillo, a Phoenix businessman. "Think of how long our border is."

A report prepared for a congressional subcommittee last year concluded that 36,000 Guard troops would be necessary to stem illegal immigration along the nation's 1,950-mile Mexican border.

That breaks down to roughly six troops per mile, rotating multiple shifts, with numbers varying depending on existing Border Patrol presence and other factors.

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"We need full-time border patrol," Napolitano said. "(Guardsmen) are there to provide support to civilian law enforcement at the border.

"They are not there to militarize the border. We are not at war with Mexico."

Napolitano's executive order spells out what duties the Guard can do at the border, including:

• Helping Arizona Department of Public Safety officers check cars going from Arizona to Mexico.

• Assisting with cargo and vehicles inspections at border crossing points.

• Helping out local law enforcement agencies in the border counties.

Republicans and other critics preferred that the plan go further by having troops take a more active role in patrolling and apprehending border crossers.

"I think all it will amount to is just a political ploy so (Napolitano) can say that she sent National Guard to the border," said David Stoddard, a retired Border Patrol agent who lives in the southern Arizona town of Hereford.

"If it's something other than that, where the National Guard is actually assisting the Border Patrol by doing something affirmative and productive, I'll be extremely pleased."

Napolitano walks a delicate line between appeasing Arizonans nervous about illegal immigration and offending a constituency that includes migrant advocates and others less supportive of ramping up border security.

Increased talk of posting the Guard on the border set off alarm bells among some immigration groups Wednesday.