Sounding a likely Republican theme for the fall congressional campaigns, House Minority Leader John J. Rhodes (R-Ariz.) yesterday blasted the Carter administration's $15 billion tax cut proposal as a "phony" which would actually add $100 to the tax burden of the average household next year.

In a speech at the National Press Club as Congress began its 10-day July 4 recess, Rhodes said the so-called Kemp-Roth proposal for a 30 percent tax cut over three years would be the Republicans' answer to the nation's economic ills, and added, "Starting here and now, Republicans intend to make sure that the American voter knows which party seeks a real tax cut and which party . . . really wants to continue a policy high taxes."

"Meanwhile, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) released an opposing statement crediting the Carter administration and the Democratic Congress with building an 18-month record of "stimulating the economy and reducing unemployment."

O'Neill said the president and Congress cut unemployment from 8 percent to 6 percent and "business fared as well as the worker under this administration." as business profits are increasing over 9 percent compared to 6 percent in the previous administration."

"This Democratic team will bring the same determination into the fight against inflation," O'Neill said, adding that both the congressional budget and levels of spending in appropriations bills are under what the president requested.

Both parties think that, this year perhaps more than usual, voter attitudes toward taxes and spending will be major factors in the fall campaigns. Both want to take advantage of the kind of disenchantment reflected in California's Proposition 13 referendum substanially cutting back local property taxes in that state.

Rhodes said the Carter tax cut figure of $15 billion would add $100 to the average tax bill because it ignore the impact of inflation and the new enacted Social Security tax increase.

Rhodes said personal tax burdens have been rising at a "record rate" of 12 percent a year since Carter took office. The Carter administration and Congress have given the American public "three consecutive years of unwanted and unwarranted net tax increases . . . the American people will take first step towards regaining control over their own pocketbooks when they elect a Republican Congress in November," Rhodes said.

Rhodes noted that President Carter threatened this week to veto a proposal by Rep. William Steiger (R-Wisc.), to cut capital gains taxes from 49 percent to 25 percent. This reflects a simplistic notion of what mades our economy go," Rhodes said. "The Steiger amendment would replenish a badly depleted pool of investment capital that we need to finance the modernizing and expansions of plants and equipment, and new endeavors that are required if we are to provide jobs for the thousands of young people entering the market each year."

The Republican leader predicted, "If we pass a tax proposal this year the Steiger amendment will be part of it" and "we will give Mr. Carter the opportunity to make good on his threat to veto it."

O'Neill avoided saying anything specific about the tax bill except that it "will be the major challenge when the House returns. We will meet the challenge."

Democratic letders will allow a floor vote on the Steiger amendment, they say , and allow Republicans to offer Kemp-Roth as an alternative tax biil. However, some Democrats want simply to extend a 1977 tax cut without allowing amendments as a way of allowing avoiding votes on the steiger and Kemp-Roth proposals this time around.

The Kemp-Roth plan is named after its leading sponsors, Rep. Jack Kemp (R-N-Y.) and Sen. William Roth (R-N.J.).

O'Neill in his recital said agreement on deregulation of natural gas prices "gives hope" an energy bill will be enacted this year.