President Reagan's proposal to raise the government's borrowing authority $50 billion ran into embittered resistance from Senate Democrats yesterday, even as Reagan paid an extraordinary visit to Capitol Hill to make a case for the debt ceiling increase and for his economic program generally.

In a related development, Sen. Bob Packwood (R-Ore.) said the spending cuts that Reagan is expected to submit to Congress in two weeks will total $12 billion to $14 billion for fiscal 1981 and about $40 billion for fiscal 1982, which some congressional budget aides said would be difficult to achieve. 1

Packwood, a Senate Finance subcommittee chairman, also said their is increasing talk of postponing the effective date of a tax cut until the 1981 fiscal year ends Sept. 30, although Treasury Secretary Donald T. Regan said as recently as Tuesday that the administration wants a tax cut this year.

A tax cut before October would make it more difficult to reduce the anticipated budget deficit of up to $60 billion for 1981, which many members of Congress consider unacceptable.

In a Senate Finance Committee session yesterday, Chairman Bob Dole (R-Kan.), said that, before a tax cut is approved, he thinks Congress should make a "down payment" on offsetting spending reductions. Some White House aides want to cut taxes right away, but Secretary Regan agreed with Dole."We simply can't have one without the other," said Regan. "They should wind through Congress together."

A new debt ceiling of $985 billion, required if the government is going to continue to pay its bills after the current debt limit of $935 billion is reached later this month, was approved yesterday by the Finance Committee and the House Rules Committee, clearing its way for action on the House and Senate floors by the end of the week.

More by necessity than choice, it is the Reagan administration's first economic initiative in Congress -- and something of an embarrassment for Republicans who have made a creer out of opposing debt increases during Democratic administrations.

With this in mind, the Democratic minority in the Senate, recalling grimly how Democrats were berated in their campaigns last fall for sponsoring previous debt-raising proposals, said many of its members will withhold their votes until it is clear that most Republicans will vote for a higher debt ceiling.

"The vast majority of Republicans would have to vote for this extenstion, or it's in trouble," said Senate Minority Leader Robert C. Byrd (D-W.Va.), who described the Democrats' tactics as an effort to "depoliticize" the debt ceiling issue.

Byrd also said the Democrats want to wait until after Reagan delivers his economic message to the people tonight and favor a less than $50 billion increase, with the figure depending on how much Reagan says he will cut the budget.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) indicated later that the vote will probably not come until Friday, thereby eliminating that problem for the Republicans.

But it was not clear whether the Democrats, outnumbered 53 to 46 by the Republicans, can muster the votes for a smaller debt ceiling increase.

Baker said most Republicans will support the increase and described the $50 billion figure as "barely adequate." Regan appeared to agree, saying the administration will probably have to come back to Congress in September to ask for another increase -- one that would carry the debt over $1 trillion.

In the Finance Committee's 6-to-3 vote for the increase, Republicans William L. Armstrng (Colo.) and Steven Symms (Idaho) joined Harry F. Byrd Jr. (Ind.-Va.) in opposing it.

Byrd and other Democratic leaders, talking with reporters after a Democratic caucus on the issue, said they were adding conditions to their support for a debt increase because they were fed up with what Minority Whip Alan Cranston (D-Calif.) called "totally demagogic, irresponsible . . . conscience-less" attacks on their votes by the Republicans during campaigns. "Now let them bite the bullet," said Byrd.

Denying that Republican's have used the issue unfairly, Baker acknowledged to reportes, however, that it is a "wrenching experience for a lot of Republicans to vote for the debt ceiling." But, he added, it is "absolutely essential."

Reagan made a straight-out pitch for support of the debt increase, as well as a more generalized appeal for his tax and spending cut package, in a 75-minute session with House and Senate leaders of both parties in the President's Room just outside the Senate chambers. Reagan aides said it was the first of several that are planned by him to keep good relations with the Republican-controlled Senate and Democratic-controlled House -- and to avoid the executive-legislative bickering that marked his initial days as governor of California.

Baker said afterward that the meeting was marked by a tone of bipartisan cooperation. "We're off to a good start . . . a good sign that augurs well for the future," he added.