California Republicans opposed to new tax increases Wednesday night caved in on a standby sales tax boost when it became clear that their soon-to-be broke state had no other way to avoid paying bills with IOUs.

Gov. George Deukmejian, who persuaded fellow Republicans in the state assembly to give him his first major legislative success, today signed the compromise tax and budget cut bill.

Although it came two days after the state technically ran out of cash, officials said only a few days of IOUs will have to be issued.

Deukmejian said he hoped some banks would offer short-term loans to eliminate the need to pay income tax refunds or bills from state suppliers with the IOUs, known as registered warrants. But John Jervis, spokesman for state Controller Ken Cory, said the state would have to pay creditors with the warrants for at least two days beginning Wednesday, at a rate of 85,000 warrants worth about $35 million each day.

If the state manages, as expected, to secure an $850 million bank loan to help pay bills the rest of the year, Jervis said, no further warrants will be necessary. By the time most warrants issued for tax refunds arrive in the mail, the state no longer will be broke and banks should be willing to cash the warrants immediately.

Deukmejian said today that with the compromise package "it is not going to be necessary to raise taxes." The bill seeks to cure a projected $1.5 billion deficit in the state's $25 billion 1982-83 budget with $640 million in tax accelerations, spending cuts and freezes, leaving the rest of the deficit for the next fiscal year.

The bill said that if more budget cuts or more state revenue from an improved economy do not wipe out the remaining $900 million deficit in the next fiscal year, the state's six-cents-on-the-dollar sales tax would have to increase by 1 cent.

California is among about 20 states struggling with budget deficits because of the economic recession and widespread taxpayer revolt, which forced California to cut real estate tax revenues severely after the 1978 passage of Proposition 13.

The legislature has spent nearly three months trying to erase the current deficit. The issue produced a sometimes bitter fight between Deukmejian and other Republicans who refused to raise any taxes, and Democrats who charged that hospitals, schools and other important services were suffering through budget cuts.

Deukmejian finally agreed to a standby sales tax increase, but only with the proviso that the tax would be reduced to 5 cents after the crisis passed so that there would be no "net tax increase." The tax returns to 6 cents as soon as the amount saved by taxpayers equals the extra amount paid during the temporary tax increase.

State officials said it would take time to assess the impact of the compromise on the state's shaky financial condition.

Standard and Poor's recently reduced the state's credit rating, forcing it to pay higher interest on the money it borrows.