The Senate opened debate yesterday on its defense-heavy spending blueprint for 1981 and quickly rejected 29 to 50, a proposal from Sen. Harry F. Byrd Jr. (Ind.-Va) to cut projected foreign aid by $500 million as as economy move.

The vote on Byrd's proposal, which would have trimmed foreign aid next year from $9.5 billion to $9 billion, came as Democratic liberals, pointing to signs of a deepening recession, began their uphill drive to get more money for social programs.

They were met head-on by Sen. Ernest F. Hollings (D-S.C.), a spokesman for the Senate Budget Committee, who launched the expected week-long budget debate with a strong defense of the big military outlay that the committee, largely at his urging, proposed last month.

"We are playing catch-up ball" with the Soviet Union, asserted Hollings, who is in line to succeed secretary of state-designate Edmund S. Muskie as the Budget Committee's chairman. "The budget proposed by the president," said Hollings, "just won't get it [the job] done."

The liberals were quick to respond, with Sen. Howard M. Metzenbaum (D-Ohio) contending that the Pentagon is awash in waste and inefficiency that must be curbed if the government is ever going to get its spending under control. The Defense Department said Metzenbaum, has an "appetite [that] inevitably rises to meet the funds available" to it.

Sen. Daniel P. Moynihan (D-N.Y.), a strong defense advocate as well as defender of urban causes, avoided the gun-versus-butter issue by proposing that $500 million be diverted to recession-prone cities from water projects, which are largely a preoccupation of western states.

Several other liberal amendments are pending before the Senate, including one from Majority Whip Alan Cranston (D-Calif.) to add about $7 billion to domestic spending for next year, to be financed in part by cuts of $2.5 billion in military outlays.

The Senate Budget Committee has proposed $155.7 billion next year for defense out of a total proposed budget package of $612.9 billion -- $7.8 billion more in military outlays than its House counterpart and $5.2 billion more than President Carter is advocating for defense.

In votes last week, the House rejected proposed amendments to its Budget Committee's recommendation from both the left and right, spurning proposals for increased defense spending as well as calls for diverting some of the military money to domestic programs.

In line with Carter's proposal to eleiminate government deficits to help fight inflation, both the Senate and House Budget committees have proposed balanced budgets as target for congressional action during the year. However, rising unemployment and other signs of an accelerating recession will probably knock the budget out of balance before the year is over, according to congressional budget experts.