The team was hoping to make the flight in anticipation of this week's World Lacrosse Championships in Manchester, England.
They were supposed to depart for England on Sunday with about 43 people, including family members.
But the British Consulate told the team Friday that it would not be given visas unless the U.S. State Department could confirm in a letter that the Nationals would be allowed back into the United States following the tournament's end, according to a press release issued by the team's board of directors.
State Department spokesman P.J. Crowley told reporters Monday that the hold-up appears to come from new security measures applied to passports -- and whether the Iroquois-issued passports meet new rules applied to travel.
Crowley said he could not confirm whether or not the passports meet new travel requirements. He referred that question to the Department of Homeland Security.
Matt Chandler, a spokesman for that department, said the agency was working to help resolve the matter with government entities including the State Department, but would not comment further.
At Tuesday's briefing, Crowley elaborated on why the team was denied the letter.
"There are specific criteria as to the circumstances under which you can provide those letters. This situation does not meet that criteria. We stand by to help them gain the kind of documents that will allow their travel to the United Kingdom," he told reporters .
"We are trying to see if there's a way to help them. The easiest way to accomplish what they want to accomplish is to get them a U.S. passport. We've been ready to do that for a number of days, and we stand ready to do that today," Crowley said.
But Dr. Percy Abrams, executive director of the Iroquois Nationals, said U.S. passports wouldn't even be accepted at the competition, where players have to produce a passport originating from the country they are representing -- the Haudenosaunee Confederacy.
Also, Abrams said, it's a matter of principle.
"We have our principles and with that sovereignty goes the idea that our country has been accepted. We've been traveling on this for years," Abrams said during team practice Monday at Wagner College in New York.
"I think it should have been explained well ahead of time or someone should have been advised that travel requirements had changed," Abrams said when asked about the update in travel security measures.
The people of the six-nation confederacy live in upstate New York. The Iroquois territory once covered most of the northeastern United States and eastern Canada.
Monday afternoon, New Mexico Gov. Bill Richardson sent a letter to the State Department and the Department of Homeland Security on behalf of the Nationals.
He asked that the matter be reviewed immediately and also noted that the passports have been used to travel outside of the United States since 1977 without problems.
"As a governor of a state with a significant Native American population, I know many tribes and pueblos will watch carefully how these young competitors are treated by the administration. As a signator of the U.N. Declaration on Human Rights, which includes the freedom to travel and return, I believe we have an obligation to assure these young men's rights are protected," Richardson wrote.
Congressman Dan Maffei, who represents the 25th District of New York, has also pledged his support to the team.
Tanya Gonnella Frichner, legal adviser to the Nationals, said Maffei was expected to meet with the State Department Tuesday evening to continue to help resolve the matter.
"He has been one of the strongest advocates," Frichner said.
The last time the team traveled outside the country was in 2002, when the championship was held in Australia. The passports didn't pose a problem then, Abrams said. But Crowley acknowledged that that was before travel requirements changed.
On Monday, Nationals General Manager Ansley Jemison told CNN that preventing the team from playing in the championship would be a "worst-case scenario for the game of lacrosse."
"These guys are also heroes to a lot of the young children that we have in our communities, and I think that would be a very negative message for the U.S. government to send to our people," Jemison said.
"We don't have a lot of heroes, and it's tough for us to have a lot of heroes... These are the 'Michael Jordans' of the native communities. These are the guys that we hold on the pedestal. These are the guys we look up to," Jemison said.
Despite the missed flight, the players are staying optimistic.
Sid Smith, a defender for the team, said the players are continuing to work hard and stay focused.
"The boys have still got their spirits pretty high and I think the morale is pretty high right now," he said.