The Senate gave final approval last night to legislation permitting the government's debt to exceed $1 trillion for the first time.

With Democrats forcing Republicans to lead the way, the Senate voted, 64 to 34, to send the House-approved measure to President Reagan, who is expected to sign it today.

Faced with expiration of the current $985 billion debt ceiling at midnight tonight, Reagan requested the new limit of $1.079 trillion, an increase of $94 billion, to cover the government's financing needs through Sept. 30, 1982.

The administration also sought, and won, a bill free of amendments that would have forced the measure back to the House, where it faced what Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) called an "uncertain future."

Before the bill passed, it was subjected to a symbolic filibuster by Sen. William Proxmire (D-Wis.) and a rash of largely Democratic attempts to attach riders, aimed mainly at curtailing the size of Reagan's tax cut, which Democrats contend will contribute to the ever-mounting national debt.

As added insurance in case of a tight vote, Vice President Bush made a rare appearance as presiding officer of the Senate, and was prepared to break a tie vote.

If the bill had not passed by tonight, the government would have been without power to borrow, forcing a financing crisis that would have meant failure even to honor Social Security checks put in the mail over the last few days, Senate Finance Committee Chairman Robert J. Dole (R-Kan.) warned during two days of debate on the bill.

Although Democrats traditionally have led the way in raising the debt ceiling to cover government obligations, and suffering punishment at the polls from Republican challengers from doing so, they were content last night to sit back and let the Senate's GOP majority provide the margin of victory, just as it did in February, when Reagan had to propose his first debt-ceiling increase.

Only after 45 Republicans voted for the bill did Democrats start voting for it in large numbers. In the end, 18 Democrats voted for passage, and only six Republicans voted against it. Of Washington area senators, Harry F. Byrd Jr. (Ind.-Va.) voted against the debt increase.

The symbolism of a trillion-dollar debt made it hard to swallow for many members. It marks a thousandfold increase over the first billion-dollar debt, registered during World War I, and an increase of more than threefold over the last 20 years. It amounts to $4,694.20 for every man, woman and child in the country, the Associated Press reported.

As the Senate moved toward passage of the landmark bill, it brushed aside all proposed riders, voting:

56 to 43 against the proposal by Sens. J. James Exon (D-Neb.) and Bill Bradley (D-N.J.) to tie the third step of the Reagan tax cut, scheduled for July, 1983, to achievement of the administration's projections of lower interest rates and a $42.5 billion deficit for fiscal 1982.

84 to 15 against making it easier for the president to win congressional approval of plans to rescind appropriated funds, as proposed by Sen. William L. Armstrong (R-Colo.), by letting the rescissions stand unless vetoed by Congress. Now both houses must approve presidential rescission to prevent money from being spent.

67 to 31 against a proposal by Sen. Thomas F. Eagleton (D-Mo.) to repeal $33 billion in tax cuts for the oil industry and transfer the proceeds to a Social Security reserve fund, which Eagleton called a move to "take from the truly greedy and give to the truly needy."

66 to 33 against a Proxmire amendment to hold the debt ceiling to $995 billion, just $10 billion more than the current ceiling, to force revenue increases and spending cuts that would assure a balanced budget in 1982.

"This wouldn't even get us through tomorrow," Dole complained in arguing against this and all other proposed amendments.

53 to 44 against a proposal by Sen. Daniel Patrick Moynihan (D-N.Y.) to advance the expiration date of the new debt ceiling from Sept. 30, 1982, to March 31, 1982, to accommodate changes necessitated by success or failure of Reagan's economic program.

66 to 31 against paring tax cuts in future years that anticipate revenue losses in excess of savings from budget cuts, a proposal advanced by Sens. Sam Nunn (D-Ga.) and Lawton Chiles (D-Fla.).

Approval of the legislation came after Proxmire talked throughout the previous night, more than 16 hours in all, to call attention to the new trillion-dollar debt and to fiscal policies he said are necessitating it.

Proxmire did not threaten the 24-hour talkathon record set by Sen. Strom Thurmond (R-S.C.) in 1957, but it was the longest talking stint by a single senator in a decade.

Republican leaders praised Proxmire's dedication, but were quick to compile figures showing that the exercise cost $64,674 in printing for the Congressional Record, overtime expenses for Capitol police and miscellaneous expenses.

Baker called the feat a "mark of Bill Proxmire's dedication and conviction, to say nothing of his stamina . . . and bladder."graphics: AP photo. Sen. William Proxmire (D-Wis) rests after 16-hour protest against raising debt limit.