George Bush accused Ronald Reagan today of making a "phony promise" that he could freeze or reverse the growth of federal spending and challenged his rival for the Republican presidential nomination to "get specific" about the budget cuts he would recommend.

Striving to regain the initiative after his drubbing by Reagan in New Hampshire and rough treatment from both Reagan and John B. Connally in Thursday night's South Carolina debate, Bush said Reagan was making "Jimmy Carter-type promises" no president could fulfill.

In a breakfast talk to businessmen in Columbia, S.C., and a luncheon address to the Chicago Executives' Club Bush repeatedly criticized Reagan by name for giving "simplistic answers" to tough economic, energy and foreign policy problems.

Citing a statement by Reagan in the Thursday night debate that the federal budget should be kept as its present size or reduced, Bush said, "There's no way you're going to have no-growth, when growth is indexed into the system" of federal benefits for Social Security and other programs. "So don't make a phony promise."

The decision to "sharpen the differences" with Reagan was made by Bush and his advisers Wednesday, the day after Reagan beat Bush by 2 to 1. But Bush failed to put the strategy into operation in the Thursday night debate, when he was kept on the defensive by charges that he was a "liberal" and by repeated rehashing of his role in excluding other Republicans from his debate with Reagan in Nashua, N.H., last Saturday.

Even in a press conference this morning, Bush's criticism of Reagan was blunted by embarrassed acknowledgements that he could be faulted for not being specific in his own past proposals.

But as he moved from sunny South Carolina to snow-clogged Chicago and then on to Boston, the gentlemanly Texan zinged Reagan more often in a single day than in his entire previous campaign.

He said the emptiness of Reagan's no-growth promise was demonstrated by the fact that the California budget grew from $4.6 billion to $10.2 billion in the eight years of Reagan's governorship.

Noting that he himself had supported the indexing of Social Security benefits to inflation when he was in Congress, Bush asked whether Reagan "wants to cut Social Security benefits for the needy and the aged."

In Columbia, he also zeroed in on Reagan's suggestion that the United States blockade Cuba until Russian troops are removed from Afghanistan.

"That's a lot of macho," Bush said, adding that a former chief of naval operations had told him that it would "take the entire Atlantic fleet" to maintain such a blockade. "How do you do that?" he demanded. "Why do you do that? Cuba didn't invade Afghanistan."

"It's a cinch to go for the punch-line out there -- the easy promise," Bush said. "But I'm going to avoid the simplistic answer."

Bush insisted here that he has not "changed strategy," but conceded that advisers felt after New Hampshire that he had to "highlight a little more" his differences with Reagan.

"New Hampshire was a setback," he said, "but it was not fatal. I am emerging as the alternative to Reagan, and from now on, I'll be homing in on him."