The Senate yesterday defeated three Republican attempts to make provision for a 10 per cent personal tax cut next year, then overwhelmingly approved a 1978 budget with a deficit of $6.1 billion.

On Thursday the House approved a 1978 budget deficit of $61.6 billion, but nearly all the differences between the House and Senate concern assumptions about how healthy the economy will be during the next 12 months.

The Senate proposed to spend only $300 million more than the House, but because the Senate thinks the economy will be less robust than does the House, it expects to pick up almost $3.1 billion less in tax collections.

The House also allowed money in the budget to permit the Congress to either increase Social Security taxes or transfer general revenues to the Social Security trust funds next year to keep the trust funds solvent.

President Carter has proposed a major restructuring of Social Security taxing - including big increases in taxes employers pay for social security and a transfer of general tax dollars to the special social security trust funds.

The Senate makes no provision for any Social Security changes next year, instead assuming that money can be transferred from trust funds which have surpluses to trust funds which need cash.

Sen. Russell Long (D-La.), chairman of the Senate Finance Committee, yesterday warned the Senate that it should have made provision for changes in Social Security financing, but said he would make no attempt to force such a change by floor amendment.

Sen. Edmund S. Muskie (D-Maine), chairman of the Senate Budget Committee, successfully fought off three Republican attempts to make provision to cut personal income taxes next year.

The moves came from Sen. William Roth (R-Del.), who merely proposed to lower the revenue floor by $11.4 billion to accomodate at tax cut, and Sen. S. I. Hayakawa (R-Calif.) and Orin Hatch (R-Utah), who coupled their tax cut provision with like-sized spending cuts.

Roth warned that unless provision for a tax cut is made now, Congress would be precluded from passing one in fiscal 1978. The President is expected to propose a vast program of tax changes within the next few weeks.

The Senate did approve, however, another Roth proposal to reduce the revenue target by $175 million to make room for a college tuition tax credit. The House approved a similar provision in its budget Thursday.

Both the Senate and the House budgets contain $6.3 billion in spending for agriculture, most of it for sharply higher farm price supports to buouy crop prices during a time of grain surpluses.

Last February President Carter proposed to spend $2.3 billion for agriculture, a figure Congress boosted to $4.35 billion when it approved its tentative 1978 budget last spring.

Both the House and Senate boosted agriculture spending to $6.3 billion to funnel larger amount of dollars to farmers whose prices are plummeting. Both Muskie and House Budget Committee chairman Robert N. Glaimo (D. Conn.) opposed the increases, arguing that farmers do not need that must assistance.