In the musical version of Anna and the King of Siam, the king describes those things that baffle him as a "puzzlement." He could have been talking about our illegal immigration problem.

With an estimated 8 to 10 million illegals who the idiocy of political correctness demands we call "undocumented aliens" now living undercover in the U.S., and a flood of documentless aliens inundating our southern borders day and night the problem has become a sword of Damocles hanging over the heads of the Bush administration, threatening to decapitate it before its second term even gets underway.

If there are such things as insoluble problems, this immigration mess fits the description. And the President is expected to solve the insoluble by executive fiat or legislative legerdemain.

This is a serious problem that has created a red hot political issue, especially in the border states. As Michael Reagan has pointed out "this is an out-of-control problem which is bankrupting our infrastructure and our hospitals. In California, Nevada, Arizona and Texas, states are being bankrupted and we have to get tough on illegal immigration which is undermining the infrastructure that was erected to take care of the citizens of the United States.

"Thanks to the flood of illegal aliens and the burden they are placing on this nation, American citizens are being increasingly denied the health care and the schooling they need because we are spending too much money on the illegals."

According to the Federation for Immigration Reform (FAIR) each year the Border Patrol apprehends more than a million people who flagrantly violate our nation's laws by unlawfully crossing U.S. borders to work and to receive publicly-funded services, often with the aid of fraudulent documents. Such entry is a misdemeanor and, if repeated, becomes punishable as a felony. Over eight million illegal immigrants live in the United States -- some even estimate that the true figure is a staggering 10 million.

An analysis of data not yet published by the Census Bureau shows that the nation’s immigrant population (legal and illegal) reached a new record of more than 34 million in March of 2004, an increase of over 4 million just since 2000.

Among the findings:

• The 34.24 million immigrants (legal and illegal) now living in the country is the highest number ever recorded in American history and a 4.3-million increase since 2000.

• Of the 4.3 million growth, almost half, or 2 million, is estimated to be from illegal immigration.

• In the data collected by the Census Bureau, there were roughly 9 million illegal aliens. Prior research indicates that 10 percent of illegal aliens are missed by the survey, suggesting a total illegal population of about 10 million in March of this year.

According to a study issued in August by the Center for Immigration Studies - one of the first to estimate the impact of illegal immigration on the federal budget based on Census Bureau data - households headed by illegal aliens used $10 billion more in government services than they paid in taxes in 2002. These figures are only for the federal government; costs at the state and local level are also skyrocketing.

The study also finds that if illegals were given amnesty, the fiscal burden at the federal level would grow to nearly $29 billion.

Among the other findings:

• Illegal alien households are estimated to use $2,700 a year more in services than they pay in taxes, creating a total fiscal burden of nearly $10.4 billion on the federal budget in 2002.

• Among the largest federal costs: Medicaid ($2.5 billion); medical treatment for the uninsured ($2.2 billion); food assistance programs ($1.9 billion); the federal prison and court systems ($1.6 billion); and federal aid to schools ($1.4 billion).

• If illegal aliens were "legalized" and began to pay taxes and use services like legal immigrants with the same education levels, the estimated annual fiscal deficit at the federal level would increase from $2,700 per household to nearly $7,700, for a total federal deficit of $29 billion.

• With nearly two-thirds of illegals lacking a high school diploma, the primary reason they create a fiscal deficit is their low education levels and resulting low incomes and tax payments — not their legal status or their unwillingness to work.

• Because many of the costs are due to their U.S.-born children, who are awarded U.S. citizenship at birth, barring illegals themselves from federal programs will not significantly reduce costs.

In an effort to cope with this problem - the new third rail in American politics - last January 7 President Bush outlined an plan to revamp the nation's immigration laws and allow some eight (or ten) million illegal immigrants to obtain legal status as temporary workers.

Under the plan:

Workers in the United States illegally could join a temporary labor "guest worker program."

• Those workers then could apply for permanent U.S. residency, but would receive no preferential consideration and would have to wait their turn.

• Employers hiring these workers must show they cannot find U.S. laborers to fill the jobs.

• These undocumented workers would get guaranteed wage and employment rights.

• These workers would receive a temporary three-year visa, renewable once. They are expected to return to their countries once their visas expire.

• Congress will be urged to increase the current annual limit of 140,000 green cards.

• The U.S. Department of Homeland Security will administer the program.

The President hotly denied that his proposal is an amnesty program.

"I oppose amnesty -- placing undocumented workers on the automatic path to citizenship," he said. "Granting amnesty encourages the violation of our laws and perpetuates illegal immigration. America's a welcoming country. But citizenship must not be the automatic reward for violating the laws of America."

Under the Bush proposal illegal immigrants already in the United States could only apply for the temporary worker program if they already have a job. The special status would last for three years and could be renewed once, for a total stay of six years. If temporary workers failed to stay employed or broke the law, they would be sent home, Bush said.

To many, this looks like a band-aid approach to a gaping wound, but it could be said that you have to start somewhere. There are as many as 10 million illegal aliens in the U.S. Does anybody know who or where they are. And even if we did, can you envision a mass round-up and deportation of an illegal population of 10 million aliens?

Like the weather, everybody talks about the problem but nobody does anything about it. President Bush may not have the ideal solution to an insoluble problem but he is at least trying.

He isn't making many people happy, especially those in the border states who are seething with anger over the all-but-open borders. If he wants to cool them off, he's going to have to tackle the illegal entry situation now and close the borders down to all but those legally entitled to cross them.

As for the 8 or 10 million already here? Well, as I said, it's a puzzlement. Maybe, just maybe, George Bush's guest worker program can de-puzzle it.