President Reagan courted conservative Democrats yesterday at the White House on behalf on his plan to cut government spending as he headed down a collision course with House Democratic leaders over the terms for voting on the cuts.

With both sides jockeying for advantage, Reagan appeared to be facing much more of an uphill fight in the Democratic-controlled House than he had last month in winning the broad spending blueprint he wanted from both houses.

Only two-thirds of the 63 conservative Democrats who helped him win in the House the first time showed up for yesterday's White House breakfast, and some of those had qualms about bolting their party a second time.

But the president had relatively smooth sailing in the Republican-run Senate. It began action on its version of the cuts-by rejecting several Democratic amendments to restore money Senate committees proposed to cut, including $925 million to retain so-called minimum Social Security benefits for current recipients.

Although Senate Democrats contended that elimination of the $122 monthly minimum payment would cause 1.8 million recipients to receive less in the way of Social Security benefits next year, their proposal was rejected, 45 to 53.

The Senate did approve, by voice vote, Democratic proposals to restore about $30 million to shield the elderly and disabled from food stamp cutbacks and to restore $69 million in 1984 to continue school lunches at orphanages and other institutions.

But it rejected another Democratic proposal to keep a new Deal-era program for foster care and adoption services from being folded into a new social services block grant to be administered by the states, with less money and fewer strings from Washington. Democrats estimated that their proposal to keep foster care as a separate program would cost $80 million. It lost, 46 to 52.

Both votes basically were along party lines, with a handful of members of both parties departing from their leaders' positions.

In both chambers the issue is spending cuts -- $39.6 billion in the Senate and $37.7 billion in the House -- that were approved by committees to meet targets established by Congress last month under pressure from Reagan.

In the Senate, the proposals face modest, scatter-hot amendments from the Democratic minority. But in the House, Reagan is seeking major changes in committee proposals, contending that the committees failed to cut deeply enough, especially in open ended entitlement programs.

While conceding that they may lack the votes to block consideration of Reagan's proposals in any form, House Democratic leaders yesterday were leaning heavily toward a strategy of allowing votes on them piece by piece, instead of permitting one vote on the package.

They figure it will be easier for members to vote against specific cuts, on popular programs than to cast a vote that could be interpreted as opposition to Reagan's overall economic program.

In his breakfast meeting with about 40 conservative Democrats, Reagan made it clear that he wanted his proposals voted on as a package.

"I think it deserves to be put before the House for an up-or-down vote," Reagan told them, adding that he has personally asked Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) to do it that way. Reagan said he hadn't gotten a response from O'Neill, but added, "Apparently I know what the answer is."

In testimony before the Rules Committee, which is considering how the measure will be handled on the floor later this week, House Majority Leader James C. Wright Jr. (D-Tex.) urged that each proposal be voted on separately. Budget Committee Chairman James R. Jones (D-Okla.) urged a "closed rule," banning all but proce durally necessary amendments, but O'Neill said the Democrats lack the votes for it.

Rep. Leon E. Panetta (D-Calif.) said the current strategy is to assemble the Reagan proposals into six or seven amendments.

Other sources said a vote on the procedures, which could be critical for both sides, is likely this week, although the amendments may not be voted on until after the July 4 recess.