House Republicans served notice yesterday that they will propose a bigger tax cut than the Democrats, with spending reductions to match, when the House takes up the fiscal 1979 budget resolution next week.

Minority Leader John Rhodes (R. Ariz.) said he thinks chances are "good" to defeat the resolution the Budget Committee will sent to the floor. Its defeat would force the committee to redraft it.

The GOP announcement suggests that this year will be a repeat of the "Perils of Pauline" drama that always seems to accompany the budget resolution on the House side.

In fact, Budget Committee Chairman Robert Giaimo (D-Conn.) says the situation is as bad or "worse" than it was last year when the first budget resolution was defeated on the House floor.

"There's a lot of moodiness in the house right now. People are angry at the president, they're angry at the leadership, they don't like the way things are going, and then here we come," Giaimo said. "There's just a taugh feeling which bothers me."

What Giaimo referred to is that although passage of the budget is a necessity, there always are large blocs of members who don't like the way the budget has come out.

Giaimo's main problem is that unlike in the Senate, where bipartisan support usually exists for the Budget Committee, House Republicans almost always vote against the budget resolution on the principle that the deficit and spending are too high.

Republicans announced a "five-year plan" to reduce both taxes and spending and balance the budget in 1983. They said Democrats were violating the "spirit" of the Congressional Budget Act by refusing to first set overall fiscal, spending and taxing priorities.

They said Democrats merely add up what they want to spend, then announce whatever deficit that incurs. Rhodes called it a "con game" that runs the process into an "automatic adding machine without a subtract button."

Generally will support a proposal by Rep. Barber Conable (R.N.Y.) to add $10 billion to the tax cut of $19.4 billion the Budget Committee has approved and support an amendment by Rep. Marjorie Holt (R.M.D.) that would hold spending increases to 6 or 7 percent above present levels.

Ironically, the Democrats have gone the opposite way on the tax cut, paring the amount from the $25 billion permanent cut President Carter wants, and Giaimo thinks it may be pared further on the floor.

Neither the Holt nor Conable amendments is expected to pass, andwhen they fail, most of the House's 147 Republicans probably will note against the budget resolution.

That means Giaimo must get all of the 200 or so votes he needs to pass it from the 288 House Democrats, and that becomes a tricky business. Many members have irrestible urges to increase spending for groups dear to their hearts. This year, for instance, there will be attempts to increase the budget for veterans benefits by some $800 million. There also will be an effort to increase programs for youth, like the Jobs Corps, and for the elderly by some $800 million overall.

The problem is that if spending is increased too much, conservative and middle-of-the-road Democrats will join the Republicans in voting against the budget. On the other hand, conservatives will attempt to increase defense spending. If this is adopted, as it was last year, liberals will vote against the budget. That was how the resolution was defeated last year.

The danger this year is complicated by the high tide of feeling running for tuition tax credits and against inflation.

The Budget Committee has included in the resolution some $1.4 billion for the president's program for more assistance to middle-class students. Giaimo will argue that the money also could be used for a tuition tax credit if that is the way the House wants to go. But the fear is that the House might leave the $1.4 billion in and vote for a tuition tax credit, too.