Wading into a subterranean battle over who gets to estimate the real cost of spending and tax bills, President Bush has threatened to veto any legislation in the next Congress that would give the power to congressional bodies rather than to the White House.

In what one official called "the first shot out of the box in what may be a year-long fight," Bush said in a letter to House Speaker Thomas S. Foley (D-Wash.) that a rule approved by the House Democratic Caucus earlier this month that would use the Congressional Budget Office and Joint Congressional Tax Committee estimates of tax and entitlement spending would "undo" last year's budget agreement.

"If the proposed rule is adopted, the House . . . will have begun the 102nd Congress by undercutting the credibility of the entire budget agreement," Bush complained in the letter sent yesterday before he left for Camp David for the holidays. ". . . I will veto any bill that contains language such as that specified in the rule."

At issue is a part of the budget deal under which the Office of Management and Budget would judge the actual costs of tax cuts or new spending for entitlement programs such as Medicare. Those costs must be offset by other changes in law to make up for the lost revenue. If that fails to occur, cuts in other entitlement programs become mandatory, a process referred to as mini-sequesters.

That provision was part of the pay-as-you-go nature of the new budget deal, aimed an ensuring that legislation that cost money would be offset by changes that pay for it at the same time. It is part of several new spending control elements built into the new budget agreement.

Under the budget pact, OMB would be the final judge of how much provisions cost and whether the mini-sequesters would kick in, a shift in power from Congress to the White House that administration officials said was deliberately negotiated into the final budget pact.

But House Democrats, in their Dec. 4 caucus, shifted the power back, giving the Congressional Budget Office the role of judging costs of entitlement program changes and the congressional Joint Committee on Taxation that power on tax legislation. The rule would become final when the full House votes on it in January when Congress reconvenes, but because Democrats control the House, its passage is assured, barring interference.

Who gets to do the count has been a major, continuing battle between the White House and Congress. Neither side trusts the estimates of the other because they are often diametrically opposed and each accuses the other of politically motivated counting.

On Bush's capital gains tax cut, for example, OMB estimated at the outset such a cut would produce more than $12 billion in revenue over six years because of stimulation of the economy. CBO, by contrast, said the provision would lose, not gain, $11 billion.

According to administration officials, House Minority Leader Robert H. Michel (R-Ill.) intends to offer an amendment to the House rules package that would eliminate the provisions shifting the cost power. Under the current package, every piece of legislation on entitlements and taxes would contain a provision that states for the purpose of that legislation, CBO or Joint committee "scoring" would be used.

What Bush has threatened to veto is any legislation that comes to him containing the offending paragraph that takes the power of judging costs out of his hands. That power, he said in his letter, was "specifically negotiated and agreed on" in the tortured, months-long process that produced October's pact.

If such provisions can be "undone before the ink is dry," Bush asked in the letter, "Where, one might reasonably ask, is the process of erosions to stop?"