Gov. Robert F. McDonnell’s $6.4 million deal to keep the Washington Redskins’ corporate headquarters and August training camp in Virginia is not sitting well with House budget-writers, who on Monday accused the governor of doing an “end run” around the General Assembly.

Members of the House Appropriations Committee gave top administration officials an hour-long, bipartisan tongue-lashing at a morning meeting, questioning whether the state really had been at risk of losing the team.

Committee members also objected to McDonnell’s pursuit of the deal — without informing legislators, they contended — after House members had twice rejected similar plans during the General Assembly session.

“He’s making a decision that’s contrary to what the vast majority of House members thought was appropriate,” said Del. R. Steven Landes (R-Augusta).

Earlier this year, administration officials briefed House budget officials on a potential deal with the Redskins. The delegates promptly shot down the idea. “We were not interested,” said Del. S. Chris Jones (R-Suffolk).

McDonnell made a second run at it later in the legislative session, when he tried to add $6 million for the Redskins to the state budget. The proposed funds were never openly tied to the team, but the administration eventually disclosed to lawmakers that was the intention. The House rejected that plan.

When the session ended, McDonnell devised a deal that taps $4 million in state funds, as well as $2 million from Loudoun County and $400,000 from Richmond. Under that deal, announced earlier this month, the team will stay in Ashburn and give Redskins Park a $30 million facelift. The Redskins’ summer training camp will shift to Richmond.

“The General Assembly and its leadership had made pretty clear that they didn’t favor this plan, and there was a lot of sentiment that it looked like an end run by Governor McDonnell’s administration around the General Assembly,” said Del. Robert H. Brink (D-Arlington) .

Said Landes: “There wasn’t a lot of support for using state tax dollars to help the company and keep them in the state. Not that folks don’t want them here . . . [but] because they’re the second most profitable NFL organization.”

Appropriations Committee Chairman Del. Lacey E. Putney (I-Bedford) and others complained that they had been kept in the dark.

McDonnell spokesman Tucker Martin said some members of the House Appropriations and Senate Finance committees had been briefed on the deal. But he also said McDonnell had the authority to pursue it on his own.

“The executive branch has the responsibility for making deals of this nature, and that responsibility was exercised,” Martin said via e-mail. “The result is a major new investment in the Commonwealth by the Redskins, the retention of the [team’s] corporate headquarters and an additional commitment by the team to another region of the state as well. This means more jobs and increased tax revenue for Virginia, and that is an extremely positive outcome in this tough economy.”

Virginia Finance Secretary Richard D. Brown and Martin Kent, McDonnell’s chief of staff, appeared before the highly skeptical committee to answer questions about the deal. That put them in the position of “spear catchers,” as Brink put it.

Brown and Kent did not present the arrangement as one that would bring new jobs to Virginia, but one that would prevent them from leaving.

“The question is, did we need to pay $4 million-plus to keep them here?” Brink said.

Administration officials said the District and Maryland had been making plays for the team. The Washington Post reported in March that District officials had launched their most serious effort in 15 years to lure the team back to its namesake city, where it hasn’t had an official presence since departing RFK Stadium after the 1996 NFL season.

But committee members said they doubted the team would have left Virginia given the relatively high corporate and income tax rates in Maryland and the District. Maryland and the District have top income-tax rates of 8.95 percent, fourth-highest in the nation. The top rate in Virginia is 5.75 percent.

“Virginia’s a good deal for them without any additional incentives,” Landes said.