Washington (CNN) -- Last week, it was Afghanistan President Hamid Karzai getting the Washington treatment -- and the pledges of long-term U.S. commitment.
But when the Afghanistan entourage exited the whirl of White House, State Department and Capitol Hill visits, you could almost hear the Obama administration take a quick breath and shout out, "Next!"
Waiting in the wings is the president of Mexico, Felipe Calderon, flying in this week for a formal arrival ceremony, a state dinner at the White House, an address to a joint meeting of Congress and an airing of the difficult issues that bleed across the U.S.-Mexico border.
When President Obama sits down with Calderon and when members of his Cabinet have separate meetings around Washington, they will certainly talk about drug violence and the Arizona immigration law.
But they also will discuss a whole host of other issues, including trade and economic challenges.
It will be the fourth time the two presidents have met for bilateral meetings.
"This is our most important relationship by far," a Mexican official familiar with arrangements for the visit told CNN. "It, of course, will have its share of pomp and circumstance, but 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 thousand of 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 will refocus attention on the $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 has arrived, maybe as little as 25 percent, according to some estimates. Some of the big-ticket items, such as helicopters and planes, are tied up in the lengthy procurement process and manufacturing schedules.
"The Merida Initiative is not perfect, but it does need to continue," said Ray Walser, a senior policy analyst at the Heritage Foundation. "There is always that question: Is that enough money and is what we are giving them effective?"
Walser is a 27-year veteran Foreign Service officer. He recently published a critique of U.S. policy: "U.S. Policy Against the Mexican Drug Cartels: Flawed and Uncertain."
He urges the two leaders not to shy away from the hard issues.
"You have to have a conversation that goes deeper that the headlines. It has to be a frank and open discussion; what are the real problems," Walser told CNN.
Walser said Mexico's progress in the war against the 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 warns 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 drug cartels.
"As 2009 began," he wrote in his 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.
"This raging brush fire in Mexico has not jumped the border, but the sparks of the crisis have resulted in violence, broken lives, and unnecessary deaths in American communities."
The Obama administration said one reason for the rise in violence is the pressure both governments are putting on drug 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 multipronged 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 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 said Monday. "I'm sure this will be discussed in detail. Whether that involves more money or just making sure that Congress fully funds the administration's proposal -- I think it's the latter."
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.
The Mexican official familiar with arrangements for the Calderon visit said he expects the president to mention the Arizona law, but 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.
"You have your loonies and we have ours, too," he said, with left wing Mexican politicians bristling at the-neighbor-to-the-north's interference in their affairs.
The United States also expects the Arizona law to be a topic between the two, according to a senior U.S. administration official.
"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, again, can only be done in a bipartisan fashion," the official said.
Olson, at the Wilson Center, noted that both presidents "are playing to domestic constituencies."
"Calderon is under enormous pressure to say something about the Arizona immigration law. How he says that in a way that doesn't feed the wrong sentiments, what level of responsibility he takes -- those are going to be important indicators," he said.
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."
Like President Karzai last week, President Calderon is expected to visit Arlington National Cemetery, to remind both countries that their relationship has been sealed in blood, not only by soldiers who died during the Mexican-American War in the 1840s, but also by Mexican-American soldiers who have fought under the American flag throughout U.S. history.
Obama told a White House audience marking the Mexican anniversary Cinco de Mayo that U.S.-Mexican bonds are unbreakable.
"They're bonds of an aspirational community -- you and your mothers and fathers, and brothers and sisters who struggled and sacrificed to realize the American Dream. They're also bonds of commerce and trade that sustain millions of jobs -- both in Mexico and in the United States."
The White House crowd applauded when he mentioned the Calderon visit.
"It's the friendship and cooperation that we'll deepen when we host President Calderon and first lady Margarita Zavala for their state visit and dinner," Obama said.