As House and Senate conferees began work yesterday on legislation to raise taxes by a record $98.5 billion over three years, both Republican and Democratic leaders said President Reagan would have to lobby intensely to win final House approval.

Rep. Dan Rostenkowski (D-Ill.), chairman of the Ways and Means Committee, warned that the president would have to put on "a full-court press" if the measure were to be enacted, and Sen. Robert J. Dole (R-Kan.), chairman of the Finance Committee, spoke in agreement.

At the conference, Dole and others signaled an interest in lessening tax increases for individuals, including the proposed reduction in the deductibility of medical expenses.

In addition, Dole said he would accept elimination of provisions that would double the cigarette tax from 8 cents a pack to 16 cents and raise the telephone excise tax from 1 to 2 percent. But he noted that this would require other, compensatory tax increases.

In addition to raising revenues, the legislation also cuts domestic spending, primarily in the Medicare program.

Dole defended the tax increases, contending that "President Reagan would not support this bill so strongly if he thought it were really a tax increase with a negative impact on investment and production."

In fact, however, the legislation takes back many of the business tax breaks enacted last year. The bill would reduce corporate tax benefits by 37.7 percent in 1986 and by 47.3 percent in 1987, the years when major business tax cuts are to take full effect, according to calculations by the American Council for Capital Formation. The business community is lobbying to postpone, rather than eliminate, beneficial tax breaks.