The White House Budget Committee rebuffed challenges from both right and left yesterday as the House prepared to work late into the night to complete its version of a target budget for fiscal 1979, which starts Oct. 1.

The economy-minded House, increasingly concerned about inflation, only narrowly rejected a Republican alternative budget that would have trimmed $13 billion from the committee's proposed $501 billion spending target that would have cut taxes by $30 billion, $10 billion more than the committee planned.

The House Budget Committee's proposed tax cut includes $7.5 billion of Social Security tax reductions and a cut income taxes by $25 billion.

Fifty-eight Democrats joined 139 Republicans to vote for the Republican alternative, proposed by Rep. Marjorie S. Holt (R-Md). The House Democratic leadership had to flex some last-minute muscle to induce seven Democrats, including Budget Committee member James A. Mattox (D-Tex.), to switch their votes. The Holt amendment was defeated 203 to 197.

The House later defeated an amendment by Rep. Barber Conable (R-N.Y.) that would have cut taxes by $30 billion without introducing any spending cuts. The conable proposal lost 239 to 163.

The committee and the leadership easily defeated an amendment by Rep. Samuel S! Stratton (D-N.Y.) to add $2.4 billion to the defense budget and another offered by liberals that would have taken $4.8 billion from military spending and given it to various human resources programs.

Aides to Rep. Robert N. Giaimo (D-Conn.), chairman of the House Budget Committee, worried before the vote of the Stratton amenment that members concerns about increasing Soviet military capability would out-weigh their worries about heavy spending. Etratton wanted to add the the $2.4 billion to enable the Navy to build another nuclear-powered aircraft carrier, which the House Armed Service Committee voted for Tuesday.

But the House rejected the Straton amendment 262 to 142. It then defeated an amendment by Rep. Parren J. Mitchell (D-Md.), to transfer spending from the military to education and other social programs.

Mitchell argued that his amendment would enable the government to create jobs for unemployed minorities, using funds he claimed the Pentagon could nexer spend.

"White America has gone back to work," Mitchell told his colleagues. "Black America is still unemployed." But the amendment was defeated 313 to 98.

The House Budget Committee has proposed a 1979 spending plan of $500.8 billion, revenues of $443.3 billion and a deficit of $57.6 billion.

Last week the Senate approved a tentative 1979 budget of $498.9 billion with a deficit of $55.6 billion. In January, President Carter proposed spending $500.2 billion and, because he wants to cut taxes $5 billion more than either the House or Senate, planned on a deficit of $60.6 billion.

The House and Senate must agree on a target 1979 budget by May 15. That budget will serve as a guide to spending and taxing legislation over the summer. By Sept. 15 both houses must agree on a binding 1979 budget.