The Senate voted 65 to 22 last night to leave room in next year's budget for a tax cut of $20 billion, which is $5 billion less than President Carter has proposed.

The rebuff to the president came only hours after he declared in his nationally televised press conference that he will not back away from his combination tax cut and tax "reform" proposal, which has run into heavy flak from several directions on Capitol Hill. (Details on Page A11.)

Carter has proposed about $34 billion in tax cuts to be offset by about $9 billion in revenue-raising "reforms," for a net reduction of $25 billion. The House Ways and Means Committee tentatively rejected many of the "reforms" last week. Yesterday the Senate voted to scale down the net cut as well.

The vote did not come directly on a tax bill, but on the first congressional budget resolution for fiscal 1979, which starts Oct. 1. That resolution sets overall tax and spending targets for Congress to shoot at while voting on specific tax and spending bills.

The Senate Budget Committee had left room in the resolution for a net a tax cut of $20 billion, partly as a way of holding down the federal deficit and guarding against inflation.The committee suggested doing this by delaying the effective date of the Carter cuts from Oct. 1 to Jan 1.

A motion to go back to Carter's larger figute was made last night by a Republican, Sen. William V. Roth Jr. (Del). Republicans have been calling for a large tax cut as a way of shrinking the government's size. Roth was supported by Chairman Russel R. Long (D-La) of the Senate Finance Committee, which handles tax legislation. Nevertheless, he lost.

All four area senators - William L. Scott (R-Va), Harry F. Byrd Jr. (Ind. Va.), Paul S. Sarbanes (D-Md.) and Charles McC. Mathias Jr. (R-Md.) - voted against the amendment.

Earlier, on a 46-to-43 vote, the Senate voted down an amendment by Sen. William Proxmire (D-Wis.) that would have reduced by 1 percent the $566 billion in spending authority proposed by the Budget Committee. The Senate earlier overwhelmingly rejected a Proxmire amendment to trim spending by 5 percent and an attempt by Sen. Carl T. Curtis (R-Neb.) to require the Budget Committee to draw up a balanced budget. The committee recommended a 1979 budget with a deficit of $56 billion.

The Senate also turned down an amendment by Sen. Thomas Eagleton (D-Mo.) that would have reduced defense spending by $1.4 billion, and another by Sen. George McGovern (D-S.D.) that would have taken $4.6 billion from the Pentagon and transferred it to domestic programs such as education and energy.

Rep. Parren J. Mitchell (D-Md.) announced yesterday that he will introduce a similar amendment to shift $4.8 billion from military to domestic spending when the House takes up its budget resolution next week.

The Eagleton amendment would have cut defense spending from $129.8 billion to $128.4 billion, the level recommended by Carter last January. The Senate Budget Committee added funds to the president's request to cover increased shipbuilding and an accelerated MX missile program, among other things. Eagleton's amendment was defeated 70 to 21, with Sens. Scott and Harry Byrd voting no and Mathias and Sarbanes voting yes.

All four voted against the McGovern move to cut $4.6 billion from military spending.

Byrd and Scott voted in favor of both Proxmire amendments as well as the Curties amendment to require a balance 1979 budget. Mathias and Sarbanes voted against all three amendments.