The chairman of the House Budget Committee warned yesterday that congressional pressure easily could push the $61 billion federal budget deficit President Carter proposed for 1979 to more than $70 billion.

Rep. Robert N. Giaimo (D-Conn.) said a deficit of $70 billion or more could come about "almost without Congress" noticing.

As a result, Giaimo said in an interview, he will join with Ways and Means Committee Chairman Al Ullman (D-Ore., in pressing for a tax cut smaller than the $25 billion package President Carter proposed for fiscal 1979, the federal spending year that begins Oct. 1.

Giaimo, who heads the committee that drafts the spending and taxing plan that ultimately rules the federal government, said that the plan the president proposed to Congress last month contains more spending cuts and higher tax levels than Congress is likely to grant.

Giaimo said he is in basic agreement with the president's proposed budget for fiscal 1979, which has been criticized by liberals for failing to increase spending for social programs, by the Republican House leadership for containing a hidden deficit of $99 billion and by some conservatives for boosting defense spending by an inadequate amount.

"The president's budget is necessarily constrained by the continuing large deficits and high rate of government spending," Giaimo said. "These factors compelled him to hold down spending growth in areas that are causing a great deal of concern."

Giaimo said the same factors will make it difficult for the House to write a budget proposal that will get enough votes to pass. Last year, the House bogged down in its first try at writing a budget for the current fiscal year.

Both Giaimo and Ullman appear to be leaning against the congressional wind in advocating a tax cut smaller than Carter's proposal.

Although Giaimo said he was not sure whether Congress would prove a tax cut smaller than $25 billion, he acknowledged that the pressure now is in the other direction.

The president's package contains tax cuts of $34 billion for businesses and individuals couple with $9 billion of revenue-raising tax reforms.

Giaimo said that tax cuts would be larger than $34 billion and it is questionable "how much of the reforms" the president will get.

Furthermore, Giaimo said, President Carter assumes Congress will pass legislation that will cut spending. Among the president's so-called legislated reforms are a lid on the growth of hospital costs, a phasing out of federal impact aid to education and a big program to reduce fraud in Medicare and Medicaid payouts.

Giaimo said that the president will fail to get many of these reforms.

"When you add all these things up, the deficit could be $70 billion or more," Giaimo warned.

On top of that, there will be pressures from a wide range of graups - spanning the spectrum from left to right - to increase spending for particular areas.

"People from urban areas says there in not enough money for urban problefs, even though there is tremendous amount of money in the budget. There is never enough. If you talk to defense interests, they'll tell you it's not enough."

The House Republican leadership has said that the president's proposed budget contains a hidden deficit that is closer to $99 billion.

Giaimo acknowledged that it will be difficult to convince Congress to vote a tax cut lower than the one proposed by the president, especially in an election year.

But he said that it will be just as difficult to defend a $65 billion or $70 billion dificit in an election campaign.

"What it (the $61 billion deficit) indicate is that what we have said it would take to reduce the deficit has not reduced the deficit, therefore we've got to take further steps to hold the line on spending and to encourage private investment," he continued.

"What we hear now," a perplexed Giaimo said, "is that the federal government must run a deficit because of the big $30 billion surplus state and local governments have and because of the massive amounts we spend overseas.

"Every year we've been told it's something else."

Giaimo warned that if the deficit cannot be reduced, the government will not have the funds to launch new, needed programs such as national health insurance and welfare reform.

Although Giaimo said he expects pressures from defense interests to provide increases in military spending beyond what Carter asked for as well as pressure from liberals to boost spending on social programs, he thinks that, with help from the White House, these pressures can be resisted.