Promising to move swiftly on tax-overhaul legislation, Senate Finance Committee Chairman Bob Packwood (R-Ore.) predicted yesterday that his committee will produce a bill similar to the measure passed Tuesday night by the House, even though President Reagan objects to major features of that bill.

Packwood and Senate Majority Leader Robert J. Dole (R-Kan.) said they doubted the Senate would be constrained by a letter from Reagan to House Republicans promising to veto the bill unless it is changed in the Senate to their satisfaction.

"I didn't write the letter. I don't mind being bound by a contract where I'm one of the parties in the contract," Packwood said. "In this case, I'm just the unwitting beneficiary of a volunteer letter somebody sent out."

Asked about Reagan's pledge to push such items as a $2,000 personal exemption for all taxpayers and dependents and a top individual rate of 35 percent, Dole said, "Those are lofty goals . . . . It's not going to be easy over here."

House approval of a bill that reduces rates while limiting deductions has put the Senate on the spot, Packwood and others said. Finding sources of tax revenue different from those in the House bill to pay for lower rates would be difficult given the restrictions Reagan and political considerations impose.

"You can only play around the edges of the bill. There's not enough money to make major changes," including those Reagan wants in the personal exemption, Packwood said.

The legislation that emerged from the Democratic-controlled House includes a $2,000 exemption for taxpayers who take the standard deduction and a $1,500 exemption for those who itemize. It has a top rate of 38 percent (Reagan wants 35 percent) and goes against Reagan's pledge in such areas as business writeoffs for investment.

Pressure from Reagan is just one of the forces that will come into play when the tax bill moves to the Republican-controlled Senate next year. Packwood, who said he plans to hold hearings in January and February and begin writing a bill in committee in March, steers a committee whose members have expressed many concerns about the specifics of wiping out deductions in order to reduce rates. Senate Finance members also have been prone to grant special tax breaks.

"I'm sure all the lobbyists are delighted it's going to be in the Senate," said Sen. Lloyd Bentsen (D-Tex.), second-ranking Democrat on the Finance panel. Bentsen said he sees little Senate enthusiasm for tax overhaul.

Administration officials planning strategy for pushing tax overhaul say that the "big ball" has been dropped in the lap of the Senate and that legislators will have to keep the tax initiative alive as long as Reagan and the Democrats keep the pressure on.

"Packwood knows the spotlight is on him," said one administration official.

The officials pointed out that the political imperative in pushing a tax bill is reversed in the Senate compared with the House. In the House, the best strategy is to work on shaping the substance of the bill in committee and then prohibit amendments that would change it on the floor. In the Senate, where one senator can block a bill, the administration is hoping to create a "governing coalition" on the floor.

To keep the public pressure on, Reagan reportedly plans to discuss tax overhaul in his State of the Union address next year.

Reagan, at the start of a White House ceremony yesterday, declared, "Tax reform is alive and well and kicking. What's that I heard about lame duckery?"

Other pressures in the Senate will include moves to change the package into a tax-increase bill as Congress struggles to meet the targets for federal deficit reduction next year. Packwood said he will not propose using the tax bill as a revenue-raiser unless Reagan specifically demands and pushes for it.

But some administration officials say they think that tax overhaul could become a tax increase in the Senate, and several members of Finance have said they would support such a change.

One device that would produce a large revenue increase in the tax-overhaul bill, restricting the the deduction for state and local taxes, which Reagan proposed and the House rejected, is considered unlikely. Packwood said that GOP senators are reluctant to take such an unpopular position on the chance that Reagan would repudiate the move, as he did earlier this year on a Social Security vote.

Sen. Bill Bradley (D-N.J.) predicts passage of a bill -- but only if Dole and Packwood give a "100 percent commitment" to the task.