Republicans reacted sharply yesterday to Carter administration charges that their tax and budget proposals do not add up.

Sen. William Roth (R-Del.) called the administration attack "totally false" and said "I would like to register a vigorous dissent" from the figures being put out by the White House on the cost of the tax proposals endorsed by Republican presidential candidate Ronald Reagan.

In a speech last night to black businessmen in Detroit, Office of Management and Budget Director James McIntyre Jr. claimed that the Reagan proposals for large tax cuts and increased defense spending, and commitments to keep retirement and Social Security programs would leave little money for other federal spending programs.

But McIntyre's figures for the cost of the tax cuts by 1985 and the likely tax revenues if taxes were unchanged were challenged by Republicans yesterday.

Rep. Trent Lott of Mississippi, chairman of the House Republican Research Committee, sent a telegram to the National Business League in which he said that the administration was unable to justify its economic record of "unmitigated disaster" and so was putting out frightening and incorrect figures for the Reagan proposals.

The administration estimates that Reagan's overall tax package would cost $285 billion by 1985. The Republican Roth-Kemp personal tax cuts would cost $201 billion while the accelerated depreciation proposals, supported by Reagan at one point, would cost $50 billion a year by then, according to Treasury estimates. The Roth-Kemp tax plan is sponsored in Congress by Roth and Rep. Jack Kemp (R-N.Y.).

The White House gets to its final figure by including various other proposals in the Republican Party platform such as the abolition of the marriage penalty.

Their figures do not take into account any likely offset due to increased revenues which would be generated by the extra growth probably sparked off by the original tax cuts. There is a dispute between the administration and the Republicans over how large the offset would be.

Roth yesterday claimed that 40 percent reflow was common although congressional sources put the figure at nearer 30 percent, which is the standard Treasury assumption. However, the reflow would be cut if there were offsetting spending cuts to balance the budget. Lott attacked the White House yesterday for raising its original estimates of the revenue loss and for putting out higher figures than those calculated by the Congressional Budget Office. White House sources yesterday denied that they had raised their estimates.

However, the Congressional Budget Office projects a "static" revenue loss -- that is, without taking into account the offset from faster economic growth -- by 1985 of only $172 billion from the Kemp-Roth cuts in personal income taxes, and $42 billion from the introduction of the accelerated depreciation proposals known as 10-5-3.

Roth said yesterday that because Reagan now has endorsed the tax-cut bill drawn up by the Senate Finance Committee, the accelerated depreciation proposals it contains, which would cost only $20 billion by 1985, give a better guide than the figures for 10-5-3.

The difference between the $172 billion figure from the CBO for the personal tax cuts and the White House figure is due to the White House assumption that Reagan would raise the brackets for income tax rates in line with inflation, as laid out in the Republican party platform.

Another discrepancy between CBO and administration figures is that the CBO projects total revenues with no tax changes of $1.077 trillion by 1985 compared with an administration figure of $1.017 trillion. The CBO believes that both incomes and profits will be higher by 1985 than the administration is projecting. In addition, the White House has assumed that Reagan would not approve tax proposals presently on the Hill that would add $36 billion to receipts by 1985.