U.S. officials suggested the flu may be spreading so quickly, there may be no practical way to contain it - and no need to tighten borders further. The disease is suspected of causing more than 150 deaths in neighboring Mexico.
At least seven people have been hospitalized with swine flu in the United States, and Richard Besser, acting director of the federal Centers for Disease Control and Prevention in Atlanta, said deaths are likely.
"I fully expect we will see deaths from this infection" as cases are investigated, he said.
The hospitalizations include three in California and two in Texas, Besser said. Later, New York said two people had been hospitalized.
Besser said the country has 64 confirmed cases across five states, with 45 in New York, one in Ohio, two in Kansas, six in Texas and 10 in California. At least four other cases have been reported by states.
Based on the latest lab analysis, Besser said new flu infections are still occurring.
He noted, by comparison, that ordinary human flu accounts for about 36,000 deaths every year in the U.S.
At an emergency hearing on Capitol Hill, infectious disease experts warned it will take at least four to six months to develop a vaccine for this new flu strain, reports CBS News correspondent Nancy Cordes.
"I think that we really need to be prepared for a worsening of this situation," said Rear Admiral Anne Schuchat of the CDC.
In California, the Los Angeles County coroner's office ruled out swine flu in the recent deaths of two men, 33 and 45 years old.
Gov. Arnold Schwarzenegger has declared a state of emergency in California, which borders Mexico, to help state agencies coordinate efforts in response to the outbreak of the illness.
In hard-hit New York, City Health Commissioner Thomas Frieden said "many hundreds" of schoolchildren are sick with suspected cases of swine flu.
The initial concentration was at a Catholic school in Queens where students recently went on a spring break trip to Mexico. But on Tuesday there were indications that the outbreak may have spread beyond the school, with two people having to be hospitalized and officials closing a school for autistic kids down the road. Those cases have not been confirmed.
"It is here and it is spreading," Frieden said. "We do not know whether it will continue to spread."
Mayor Michael Bloomberg said that 82 of 380 students at P.S. 177, a school for autistic children, have called in sick. A third school in Manhattan is being evaluated because students there are sick, Frieden said.
Mexico late Tuesday said that the number of suspected swine flu deaths has risen to 159, with the virus confirmed as the cause of death in 26 of those cases.
Health Secretary Jose Cordova says 2,498 suspected cases of swine flu have been reported, with 1,311 of the patients still in the hospital.
Cordova said authorities have instituted rapid testing to generally rule out other types of flu and start anti-viral treatment more quickly in swine-flu cases. The tests to definitively determine swine flu are time consuming.
Mexico announced further measures to stop the spread of the virus Tuesday, putting its famed pre-Columbian pyramids and all other archaeological sites off limits nationwide and.
Throughout Mexico, there is growing frustration that the full scope of the epidemic has not been revealed, reports CBS News correspondent John Blackstone from Mexico's capital.
The government says it started April 13 with a woman in Oaxaca. But, Blackstone reports, people in Vera Cruz claim it began almost four weeks ago in their village near a large pig farm outside Mexico City where a four-year-old boy, since recovered, may have been the first victim.
In Canada, which also borders the U.S., health officials confirmed a total of 13 cases of swine flu, which Canadian Health Minister Leona Aglukkaq said were mild and have links to Mexican travel. The Canadian government warned against unnecessary travel to Mexico.
Some countries are taking bolder measures. Argentina said it is suspending flights from Mexico as a precaution against the spread of virus and wants tens of thousands of visitors from North America to report to the Health Ministry.
Cabinet Chief Sergio Massa says the measure is in effect until Sunday at midnight to "transmit a sense of calm to Argentines."
He called Tuesday on the 60,000 visitors from Canada, Mexico and the U.S. who have arrived in Argentina in the past 20 days to contact the Health Ministry, which will take measures to control a possible spread of the virus.
The EU's disease control agency as well as Israel and France also warned against nonessential travel to Mexico, while Cuba suspended flights to and from Mexico.
In addition to countries in North America, other nations with confirmed swine flu cases include Scotland, New Zealand, Spain and Israel.
While Mr. Obama requested additional money from Congress to build drug stockpiles and monitor future cases, other U.S. officials suggested the flu may be spreading so fast that stepped-up border security may not help.
Homeland Security Secretary Janet Napolitano, interviewed on NBC, said officials "anticipate confirmed cases in more states."
She reiterated Mr. Obama's statement on Monday as he grappled with the first domestic emergency of his presidency - that the spread of the disease is a cause for concern but not alarm.
Asked about stricter measures, Napolitano pointed out that the U.S. does a great deal of trade with Mexico and "that would be a very, very heavy cost for - as the epidemiologists tell us - would be marginal, if any, utility in terms of actually preventing the spread of the virus."
Fear is running high, prompting some people to stock up on masks and antiviral drugs like Tamiflu, reports CBS News medical correspondent Dr. Jon LaPook.
"Yesterday, everybody was looking to get Tamiflu," said pharmacist Martin Keane. "We had some in stock, but we haven't been able to obtain any from our wholesalers."
Experts warn that inappropriate use of Tamiflu could make it stop working, LaPook reports.
Meanwhile,hoped to have a key ingredient ready in early May, but were finding that the virus grows slowly in eggs - the chief way flu vaccines are made.
Even if all goes well, it still will take a few months before any shots are available for the first required safety testing, in volunteers.
"We're working together at 100 miles an hour to get material that will be useful," Dr. Jesse Goodman, who oversees the Food and Drug Administration's swine flu work, told The Associated Press.
As health officials moved to try to slow the spread of the new virus, U.S. agriculture officials suggested it would be a good idea to change its name from "swine flu" to avoid the misconception that pork products may be affected.
Agriculture Secretary Tom Vilsack points out that the virus is not food-borne and has nothing to do with consuming pork. Vilsack says he's concerned that misunderstandings could have a negative impact on farmers.
With pork prices falling, government officials went to great lengths today to point out that not a single hog in the U.S. has tested positive for the virus, reports Cordes.
"It is perfectly safe to consume pork products from America," Vilsack said.
The disease has been called swine flu because the underlying virus contains genetic material from swine; but it also contains genetic material from birds and humans, scientists say.
Swine Flu News Worldwide: