Seven times in the eight years they held office, Republicans Richard M. Nixon and Gerald R. Ford vetoed the giant Labor-Health, Education and Welfare appropriations bill - the bill that provides funds each year for the Democratic Party's favored social welfare programs.

Now, though few outsiders have noticed the building confrontation, it appears that Democrat Jimmy Carter, too, may be pushed to veto this important symbolic legislation.

Ever since taking office, the new President has been drawing spending limit lines in the dust and warning his disbelieving fellow Democrats in Congress not to cross them.

He warned them not to go beyond the price support levels he proposed in the farm bill - but both House and Senate Agriculture committes have done so anyway.

He warned them not to include funds in the upcoming public works appropriations bill for the water projects he opposes - but the House Appropriations Subcommittee on Public Works has disregarded this warning, too.

The problem bill that seems likely to reach his desk first, however, is neither of these two, but the Labor-HEW legislation.

A House Approriations subcomittee has approved a spending level of the coming fiscal year that for HEW alone, is $1.4 billion over Carter's recommendation (which, in turn was already $1.7 billion than Ford has originally asked.).

If anything, the Senate is expected to go even higher than that; it traditionally appropriates more than the House on this measure.

These amounts have Carter aides worried - so much so that when he returned from Europe last week, he found on his desk a memo from his Office of Management and Budget describing the Labor-HEW legislation as "a serious problem."

For a Democratic President facing a Democratic Congress, a veto of this key domestic spending bill would be, as one Carter aide wryly understated it several days ago, "a serious political problem that should be avoided."

But as an HEW official observed, Congressed in the last eight years of divided government has become "used to setting education and health spending policies. And they are in a mood to change, even for a Democratic President."

And the HEW bill would run roughshod over Carter's stated objective of balancing the budget by fiscal 1981, four years from now. As one OMB official put it, for a President "trying very hard to get to a balanced budget, that is now way to do it."

What has stirred particular White House attention, one aide recalled, are some major subcommittee increases for HEW that were " explicit attempts to ovrride decisions of the President."

These White House budget concerns are all shared in HEW itself.

"The people in the (HEW) program areas are delighted" with the subcommittee's higher spending figures, a department official said. "There has been a lot of end-running by (HEW) people pushing for their favorite thing."

For years, Congress has worked behind the scenes with HEW bureaucrats to set appropriations higher than White House recommendations.

This silent coalition has led to increased budgets and the seven vetoes of Labor-HEW appropriations since the GOP took over the White House in 1969. Four were overriden by Congress including Ford vetoes the past two years.

The Carter White House is keenly aware of this history: HEW Secretary Joseph A. Califano Jr. has had calls, according to OMB officials, tellihg him to keep the bureaucrats in line.

White House congressional liaison aidea are being put to work in an effort to get the full House Appropriations Committee to make some cuts in the subcommittee totals when the Labor-HEW money comes up for markup.

But White House sources don't expect to have much success in the House, or in the Senate either.

The three largest increases voted by the House subcommittee were in programs that Carter specifically wanted eliminated or slowly phased out.

Carter provided no funds, of example, for the National Defense Student Loan program, which provides a revolving fund to colleges. School administrators, then, lend the money to students of their choosing.

The Carter position was that repayment of earlier student loans from the NDSL program would amount to $276 million next year. That, along wigh other new and expanded federal loan programs aimed at the underprivileged would make up for a cutback in NDSL funds to the bill.

Another program the Carter budget slashed was impact aid - funds that for years have gone to shool districts with federal employees, and now go to most school districts in the country.

Other Presidents have tried to cut back this program and failed. The subcommittee quickly put $405 million back into the bill for impact aid.

Carter aides expected to lose this one but plan to try a phaseout next year. This year's trade-off - taking $350 million from impact aid and putting it into Title I elementary school funding - backfired.

The subcommittee not only added $405 million for impact aid, it kept the $350 million Title I "Trade-Off" and added $100 million of its own.

In the health area, the subcommittee's biggest increase also came in an area Carter tried to phase down - aid to health professional schools.

Here, again, the Carter effort was to cut down "on the multiplicity of little programs which aid some but on a non-income test basis," an OMB official said.

The Carter OMB argument was that nurses and other health professionals could be aided by general student aid programs that were distributed on the basis of financial need.

"Why should nurses who can afford schooling get special aid?" a Carter aide asked.

The subcommittee's response, according to a House aide, was that the country needed more of these people trained, no matter what the individual student's financial status.

Defeat for the President on these three items was a harbinger of problems he is likely to face on next year's budget, the first he will draw up on his own. He must hold spending in close check next year to move toward a balanced budget. That may be an added reason for insisting on restraint this year, too.