President Reagan invited the entire Senate to the White House yesterday to lobby for a sweeping overhaul of the tax system, only to find himself preaching to the choir.

Senate Minority Leader Robert C. Byrd (D-W.Va.), among others, told Reagan he expects a 100-to-0 vote for the radical tax bill, which would slash tax rates in exchange for eliminating many deductions.

"I believe we're on a roll," Majority Leader Robert J. Dole (R-Kan.) said after the breakfast. He and Finance Committee Chairman Bob Packwood (R-Ore.) said they plan to bring the bill up on Monday and hope to take the final vote by the end of next week -- an unusually fast pace for a tax bill.

However, congressional aides who were drafting amendments to the bill yesterday -- about 20 to 30 are expected -- predicted that debate over changes could last until late this month. Reagan urged the 75 senators who came to breakfast to keep the bill bipartisan, but did not ask them to oppose all changes.

Packwood and Dole have been lobbying fellow senators to defeat all amendments in hopes of preserving the bill's maximum rates of 27 percent for individuals and 33 percent for corporations. Hill aides predicted, however, that any changes would be balanced by closing loopholes, not by raising rates.

Those backing amendments to preserve full deductions for Individual Retirement Accounts appeared to have the strongest momentum. But those amendments must be balanced by tax increases, which are likely to alienate many constituencies, Packwood emphasized. "The question is not: Is an IRA amendment popular? The question is: as opposed to what?" he said.

Sen. Russell B. Long (D-La.), ranking Democrat on the Finance Committee and a former chairman of that panel, praised the bill as "the best revenue bill ever reported out of a committee" and vowed to support Packwood in the floor debate "even if he's wrong." He also predicted a 100-to-0 vote.

Sen. Bill Bradley (D-N.J.), an early advocate of tax overhaul, said, "It's very helpful to have that many senators in the room with no negative noises at all, and leaders saying it could pass 100 to zero.