The group says ground must be broken early next year in Shanksville, Pa., in order for a memorial to be build for the 10th anniversary of the crash in 2011.
Svonavec Inc. owns one of the last large chunks of land needed for the 2,200-acre memorial, including the area where the plane crashed Sept. 11, 2001. Svonavec's treasurer Mike Svonavec has said the park service has not done enough to negotiate a deal. He did not immediately return a call for comment on Sunday.
White said Svonavec has not been willing to negotiate, and called that unacceptable.
"We've certainly sought to do this within in the process, following protocol as much as we possibly can," White said Saturday. "It has gotten to the point where we fear we'll lose significant momentum.
"We have an administration that has been very supportive of this effort. We just wanted to make sure the president is aware of what the circumstances are. ... We just didn't want to get lost in the shuffle."
The White House said it was reviewing the letter.
"The president recognizes the contributions of those working to memorialize the heroes of Flight 93 with a fitting tribute at the spot where they gave their lives to ensure that others would live," Pete Seat, a spokesman for the White House, said Sunday.
Bush signed legislation authorizing the building of a national memorial to the passengers and crew of Flight 93 on Sept. 24, 2002. The president has twice visited Shanksville, Pa., to mourn with those that lost loved ones.
In October, the National Park Service said it would use an independent appraiser to determine the value of 275 acres of land needed for the memorial. The NPS also said it could use eminent domain to acquire the plot if all else fails.
Construction of a $58 million permanent memorial and national park is scheduled to begin in 2009.
White, whose cousin Louis Nacke II died on Flight 93, said the group would favor Bush giving the interior secretary or director of park services the power to take the necessary steps to acquire the land before the administration leaves office in January.
He said the families understand that the outgoing president has plenty to do in his final weeks in office. But White pledged that the group would carry its fight to the Obama Administration, if needed.
"I think the rest of the family members and I feel there is no point at which we will stop," White said. "Whatever it takes. As long as it takes. Whoever it takes. To do anything less would be doing a disservice to those that we love."
Flight 93 was en route from Newark, N.J., to San Francisco on Sept. 11, 2001, when it was diverted by hijackers. The official 9/11 Commission report said the hijackers crashed the plane as passengers tried to wrest control of the cockpit.