Just days after they were outfoxed by conservative Sen. Jesse A. Helms (R-N.C.) in restoring money for school lunch programs, Senate Democrats are facing the prospect of being upstaged by a low-profile Republican moderate or more of their pet budget issues -- from education to fuel assistance for the poor.

As the Senate moves today into its third day of action on President Reagan's proposed budget cuts, the outnumbered Democrats fear they have little if any chance of restoring money for Democratic-initiated social programs that the Budget Committee wants to cut in accord with Reagan's wishes.

The best chance for a general salvage operation appears to be a plan by Sen. John H. Chafee (R-R.I.) and other GOP moderates, mostly from the Northeast and Midwest, to restore about $1 billion for programs such as elementary and secondary education, fuel assistance, weatherization, urban development projects, mass transit and community and mental health.

If Chafee proceeds as planned, it could mean a split in the ranks of the Republican majority, which has been remarkably united on most issues in the budget debate -- foreign aid being the conspicuous exception.

But Chafee's plan has the countervailing political advantage of beating the Democrats at their own game, with credit going to Republicans from the region Democrats contend the budget cuts will do the most harm, primarily the older industrialized states.

And, if the Chafee forces get their way, it will not violate Reagan's overall savings target, which the Budget Committee has translated into a set of instructions to legislative committees to pare back spending programs by $36.4 billion for fiscal 1982, or roughly $87 billion for the three fiscal years from 1981 to 1983. According to its arithmetic, the committee actually proposed cutting $2.3 billion deeper than Reagan did for fiscal 1982.

This provides a little leeway for add-ons, especially if the Senate does not go all the way in putting back $3 billion for filling the Strategic Petroleum Reserve. The Budget Committee proposed eliminating the $3 billion, but the Energy Committee wants it restored. The Senate is reported to be closely divided on the oil reserve issue, and, because the Senate does not appear to want to outspend Reagan, the outcome could help determine the fate of the Chafee effort.

The role of Budget Committee Chairman Pete V. Domenici (R-N.M.) in the continuing negotiations over the Chafee intiative could be crucial, according to Republican aides. Although, new to leading budget floor fights, Domenici has displayed deft control so far. Chafee's people say Domenici's staff has been helpful to them, but Domenici is holding his cards close on the issue.

Perhaps significantly, an aide to Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said Friday that Baker may support the Chafee effort.

The Democrats are carrying around amendments that would restore more money for social programs than Chafee would, but their record in two days of voting on budget cuts is not auspicious. They lost three bids to provide more money for veterans health programs than Reagan wants, and their plan for a crusade to restore $400 million for school lunches was derailed Friday by Helms.

Helms beat them to the punch with a proposal to add $200 million for school child nutrition programs, which Reagan had proposed cutting by $1.6 billion, and forced them to swallow an offsetting $200 million cut in foreign aid in the process.

Aides to Chafee said he introduced an amendment proposing about $1.1 billion in added funds for social programs on Friday but is still consulting with colleagues on details. Whether Chafee will push ahead with floor action on the proposal is expected to hinge on more consultations today.