Balanced budget and flat-rate tax are popular, but

Remember the balanced-budget amendment? Though guest of honor at a flag-waving presidential rally in July, the measure is now mired in the House of Representatives.

Remember the flat-rate tax? Once it was as fashionable as aqua miniskirts. Now Sen. Robert Dole, Finance Committee chairman, says Congress is unlikely to consider a serious flat-rate tax bill before 1985.

Both these ideas swept through Washington this summer like winds from the Great Plains. The American populace had exaggerated hopes for these issues, say some Washington observers - hopes which reflected the public's sometimes contradictory attitudes towards federal spending and deficits.

''They are both populist movements,'' says Tom Field, executive director of Tax Notes. ''The balanced-budget amendment is way out front there - but the flat-rate tax clearly strikes a chord with the public. (If they became law), goodness knows the public would be disappointed (with the results).''

Both issues are far from dead. The balanced-budget amendment will almost certainly remain trapped in the Judiciary Committee chaired by Rep. Peter Rodino (D) of New Jersey until the end of the 97th Congress. But proponents say it will be reintroduced next year - and they say they will continue to prod state legislatures in an effort to call a constitutional convention on the subject.

At least 10 flat-rate tax bills are currently pending in Congress. Hearings on the subject begin this week, but Senator Dole has cautioned that Congress is unlikely to move quickly on the issue.

Broad-based criticism has slowed the progress of these sweeping economic reform efforts. American Enterprise Institute economist Rudolph Penner - no free-spending liberal - has said that the balanced-budget amendment won't work, because it simply requires Congress to adopt a balanced budget on paper and contains loopholes that would allow actual spending to continue running in the red.

The flat-rate tax has yet to receive thorough congressional scrutiny. Many economists claim the public doesn't yet realize that a pure flat-rate tax would increase the taxes of those making less than about $50,000.

''Clearly, it would mean a very large tax cut only for those at the top,'' says Joseph Pechman, Brookings Institution director of economic studies.

Most economists say that when the public gets a good look at the flat tax, it will decide a progressive system isn't so bad after all. Support for the balanced-budget amendment, they say, is much more deeply entrenched. Last June a Gallup poll showed that almost three-fourths of respondents thought such an amendment should be part of the Constitution.

Analyzing this support, a just-released Congressional Budget Office report finds that Americans' attitudes toward federal spending ''have formed a remarkably consistent, if contradictory, pattern over time.''

The CBO report says the vast majority of Americans over the past 50 years have been consistently in favor of spending increases in most areas of government activity. The Gallup poll, which found strong support for the balanced-budget amendment, also found healthy majorities opposed to spending cuts in such activities as defense, health, and education.

This contradiction springs from the fact tht most US citizens have no idea of the relative costs of federal programs and feel the budget can be balanced by simply getting rid of waste and fraud, the budget office says.

Seventy-one percent of those responding to a 1979 NBC-Associated Press poll agreed with the statement: ''The federal budget could be balanced just by reducing waste and inefficiency.''

Last year, the CBO estimated that about 4 percent of the budget ($24 billion for 1981) represented waste. Adm. James Nance, director of the President's Private Sector Survey on Cost Control, says, even on his waste-hunting panel, ''nobody's talking about balancing the federal budget by cutting waste, fraud, and abuse.''

So politicians, caught between their constituents' expectations and the realities of governing, are forced to ''balance the people's infinitely numerous wants . . . against their normal and natural reluctance to pay higher taxes,'' the CBO concludes.