Gov. Rick Perry said the deployment to Texas was "insufficient to meet the needs of securing the Texas-Mexico border."
Arizona Gov. Jan Brewer, a Republican like Perry, also wasn't happy with the plan.
"What we heard wasn't anything what we hoped to hear," she told reporters after a 90-minue briefing by federal officials sent by President Barack Obama.
A White House statement said plans to deploy 1,200 additional National Guard soldiers along the U.S.-Mexico border would "complement the unprecedented resources and additional efforts already devoted by this administration to securing the Southwest border."
Arizona would get 524 National Guard troops, Texas would get 250, California 224 and New Mexico 72, officials said. Another 130 would be at a national liaison office.
Brewer has said the deployment should total 6,000, including 3,000 in Arizona, the state with the most illegal border crossings.
Perry asked in January 2009 for 1,000 National Guard troops to help with border security in Texas alone.
"Texas will continue to urge the federal government to provide the necessary resources so the brave men and women of the Border Patrol can effectively do their jobs and protect our border communities, and the entire nation, from those who would do us harm," Perry said.
He said only about 20 percent of the deployed troops will come to Texas, which has 64 percent of the U.S.-Mexico border.
The White House statement said the extra Guard troops would be used to provide intelligence surveillance and reconnaissance support as well as backup to counternarcotics enforcement until more civilian officers are trained and stationed at the border.
The federal officials briefed Brewer, her senior aides and several state agency heads after an hourslong meeting in Tucson earlier Monday with Attorney General Terry Goddard, U.S. Rep. Gabrielle Giffords and dozens of local law enforcement officials. Goddard and Giffords are Democrats.
The federal team was led by John Brennan, a national security adviser whom Goddard said has the job of evaluating "the whole picture."
"He never said, 'This is all,'" Goddard said. "He said, 'This is what we're going to do right now.'"
The meeting with Brewer resulted from her June 3 visit to the White House, where she and Obama discussed border security and immigration. Brewer asked for specifics on plans for Arizona.
The president previously announced plans to send 1,200 troops to the border, and he asked Congress for $600 million to pay for 1,000 more Border Patrol agents, 160 new federal immigration officers and two unmanned aircraft. The figure includes $500 million in new spending and $100 million of redirected spending.
Brewer said after the June 3 meeting that Obama gave assurances that the majority of the 1,200 troops would go to Arizona. She sought them to help stem the flow of illegal immigrants and drug smugglers across the border, and she reacted to Obama's initial announcement by saying 1,200 wouldn't be enough. She also urged Obama to send National Guard helicopters and surveillance drones to the border.