President Calderon criticized the Arizona law during his welcoming ceremony

Washington (CNN) -- President Obama rolled out the red carpet for his Mexican counterpart, Felipe Calderon, at the White House Wednesday morning as the two leaders prepared to tackle a range of pressing issues, including immigration, crime and trade.

Calderon was welcomed by Obama, Vice President Joe Biden and Secretary of State Hillary Clinton in a formal arrival ceremony on the South Lawn.

U.S. first lady Michelle Obama and Mexican first lady Margarita Zavala also joined their husbands for the occasion, which will be followed by a state dinner Wednesday night.

The United States and Mexico "have forged a new era of cooperation," Obama said. "We are defined not by our borders but by our bonds."

Calderon noted the two countries are facing a series of common challenges, including immigration, climate change and organized crime -- a rising threat to border stability.

He criticized Arizona's controversial new law designed to crack down on illegal immigration, arguing that it is causing "our people to face discrimination."

But "what turns us into good neighbors is everything that we share: freedom, justice, and democracy," he said.

The meeting marks the fourth time the two presidents have met for bilateral talks.

"This is our most important relationship by far," a Mexican official familiar with arrangements for the visit told CNN. "It will build on the relationship established by President Calderon first with President Bush and now with the new administration."

The official did not want to be identified because he was not authorized to speak about the visit.

Washington experts agree the visit is a chance for both sides to polish an increasingly important relationship.

"You need to reaffirm it often and strengthen it," said Eric Olson, who analyzes the U.S.-Mexican relationship for the Woodrow Wilson Center. "Like a boyfriend and girlfriend in high school -- if you don't keep reaffirming it, then you worry things aren't what they should be."

Part of the relationship is the shared concern about illegal drugs and related violence. Drug violence claimed 6,500 lives in Mexico last year. About 90 percent of the cocaine that is smuggled into the United States moves through Mexico, which is also a gateway for marijuana and other illegal drugs.

Moving in the other direction, Mexican authorities in recent years have seized 45,000 weapons that could be traced to the United States.

The Calderon visit also refocuses attention on a $1.3 billion aid package known as the Merida Initiative, agreed to in 2007 with the first appropriations approved by Congress in June 2008. The aid is a mix of hardware -- helicopters and ion drug scanners -- as well as efforts to beef up Mexican courts and other institutions.

Despite congressional action and agreements between the two counties, only a fraction of the aid actually has arrived, maybe as little as 25 percent, according to some estimates. Some of the big-ticket items, like helicopters and planes, are tied up in the lengthy procurement process and manufacturing schedules.

Ray Walser, a senior policy analyst at the conservative Heritage Foundation, recently argued that Mexico's progress in the war against drug cartels is tempered by uncertainty about the adequacy of police and judicial reforms, the persistent problem of corruption and the danger of a loss of political will to continue the drug fight.

Like many other experts, Walser warned that the United States must commit resources to reduce U.S. drug consumption while at the same time assisting Mexico in its fight against the cartels.

"As 2009 began," he wrote in a recent critique, "many in Washington worried that Mexico hovered on the brink of a narco-collapse or state failure. Without a doubt, Mexico has weathered an extremely tough year and will look back in horror at the more than 9,000 dead and associated costs imposed by President Calderon's war against narco-traffickers."

The Obama administration said one reason for the rise in violence is the pressure both governments are putting on the cartels.

"The pressure that the Calderon administration has placed on the DTOs [drug trafficking organizations] has certainly generated a great deal of violence as those organizations fight for more restricted access to the United States in terms of the drug market," said a senior administration official who briefed reporters Wednesday on the condition of not being identified.

"But putting pressure on the DTOs is an important part of a multi-pronged strategy to create a lasting dismantlement of these organizations that generate crime and violence in Mexico and have deleterious effects in the United States as well."

Olson says one risk of high-level meetings like the one this week is that they may raise expectations to unrealistic levels.

"There may be expectations of new initiatives, which I don't think there really is going to be," he said.

U.S. State Department spokesman P.J. Crowley said Monday that the focus is changing in how the United States aids Mexico in the drug fight.

"We are shifting the emphasis from the purchase of heavy equipment to training for, and strengthening of, Mexican institutions of government," Crowley noted. "I'm sure this will be discussed in detail."

Another hot issue is immigration, especially with the spotlight burning brightly on the new Arizona law cracking down on illegal immigration and giving police new authority to determine immigration status. Mexico has issued a travel alert to Mexicans about visiting, residing or studying in Arizona.

But a Mexican official familiar with arrangements for the Calderon visit cautioned that it would be wrong to let that overwhelm the rest of the visit.

"It will not define the visit or the relationship," the Mexican official said. "The U.S.-Mexican relationship is much more rich and diverse than one issue."

He explained that both presidents have domestic pressures that pull them in different directions.

A senior Obama administration official said, "we certainly understand that this is an issue that has resonated in Mexico, is of deep concern to the Mexican government, and, again, underscores the importance, as the president has said, of dealing with that frustration in the United States, fixing our broken immigration system and moving forward with comprehensive immigration reform that ... can only be done in a bipartisan fashion."

Earlier this month, Mexico's ambassador to the United States, Arturo Sarukhan, warned of what he called "a worrying surge" of anti-immigrant sentiments. He warned that the Arizona law might "poison the well from which our two nations have found and should continue to find inspiration for a joint future of prosperity, security, tolerance and justice."