Money for a second tax bill this year will come from faster-than-predicted economic growth, Treasury Secretary Donald T. Regan said yesterday. This comment is likely to increase congressional fears that there may not be room for a second bill, which President Reagan has promised would contain a variety of tax-cut favorites.

Meanwhile, nominees for two top Treasury posts disagreed radically in confirmation hearings yesterday over prospects for the economy. Norman Ture, a fervent supply-sider and the designated undersecretary for tax policy, told the Senate Finance Committee that the president's tax proposals will have a "very strong expansionary impact" on the economy, "very promptly."

In contrast, Beryl Sprinkel, an equally fervent monetarist and designated undersecretary for monetary affairs, told the committee that the restrictive money policy favored by the administration could lead the economy to "flatten out and sag for a while."

The administration has been widely criticized for making an overoptimistic assessment of how the president's program will affect the economy. But Regan said yesterday that be believes the official forecasts published with the president's program were "conservative." There probably will be more growth, and more "reflow" back to the Treasury from the main tax proposals than the administration has allowed for, he said.

President Reagan has promised that if Congress passes a "clean" tax bill along the lines of his proposal, he will put forward a second bill including such measures as tuition tax credit, a reduction in the so-called marriage tax penalty affecting many two-income families, and special savings incentives.

The administration predicts a huge boost in savings and investment if its economic program is enacted. Treasury Secretary Regan yesterday gave details of the dramatic increases expected, on which many of the rest of the administration's assumptions are dependent.

Personal saving will rise sharply from recent low levels of less than 6 percent of personal spendable income to an average of 7 percent between 1981 and 1986, the Treasury secretary said. A steady rise in this saving rate is predicted from the 5.6 percent level last year to 7.9 percent by 1986.

Perhaps even more startling is the projected rise in business investment to 15 percent of the whole economy, as measured by gross national product, by 1986. In the last five years, business fixed investment has averaged about 11 percent of GNP, itself a higher figure than in either of the two previous decades.

The administration's savings and investment figures are consistent with the overall economic forecasts published last month with the president's economic recovery program, a Treasury official explained yesterday.

Business would have to increase its investment at an unprecedented rate of about the rate of inflation in order to match the administration's forecasts, according to testimony given by the Treasury secretary last month. An even faster rise would seem to be necessary to achieve the 15 percent share in GNP by 1986.