Reagan open to tax hike if his program isn't hurt

President Reagan said he would consider tax increases as part of any budget compromise with Congress, but would not accept proposals that altered the basic thrust of his economic program. In a speech to the US Chamber of Commerce, the President said he is standing firm on his commitment to increased defense spending, a three-year, 25 percent income tax cut enacted last summer, and further reductions in government spending.

Mr. Reagan stressed anew his opposition to calls for a freeze on nuclear arsenals, saying: ''A freeze is not good enough. . . We must have mutual and verifiable reductions and this we shall strive for.''

Chief Justice Warren Burger, also speaking to the group, urged US authorities to adopt rehabilitation techniques used in European and Soviet prisons, stressing compulsory education and job skills.

Mr. Burger said that in American prisons inmates are usually given no skills, unlike European penal institutions he has visited where job training is enforced. He noted it costs $10,000 to $30,000 a year to keep a US inmate in prison. ''This isn't a matter of pure compassion, but good frugal sense,'' he said.