In the frantic, final days of the presidential campaign, Ronald Reagan is stepping up his pressure on the industrial states, while Jimmy Carter must interrupt his courtship of big-state Democrats to repair his fragile southern base.

"It's a problem, for us, having to go back into the South at this late date," one Carter adviser conceded. "But that's the way it is."

After working the overwhelmingly Democratic garment district of Manhattan yesterday, in a bid to lock up New York's 41 electoral votes, Carter wound up his day of campaigning in Columbia, S.C. He will spend the next two days working his way, one more time, through Florida, Tennessee, Mississippi, and Texas -- all states that he carried in 1976, and all states that he is either trailing in or finds uncomfortably close in 1980.

Carter yesterday toured the spiritual heartland of the old Democratic coalition, preaching against the evils of Republicanism and reminding Democratic voters that he, too, is a Democrat. Reagan, meanwhile, accused his rival of ineptitude, vacillation and manipulating budget figures to conceal the size of the federal deficit as he moved quickly through five southern and eastern states.

This race between Carter and Reagan remains a contest in which there are many states, large and small, that are too close to confidently call. And the Carter officials concede that they would have much preferred to spend most of their time in this last week stumping through the large industrial states of the north and the Great Lakes.

But instead, for the next couple of days, Reagan will be able to concentrate on this area that is America's electoral vote heartland, while the president tries to convince his fellow southerners to vote for him once again. Reagan will be working Pennsylvania, Illinois, Wisconsin, Michigan and Ohio through Sunday.And most of his time in those states will be devoted to working the white-collar suburbs, hoping to shore up support among Republican voters that his strategists think is still his, but which is nevertheless considered to be "soft."

In the stretch drive of this race for the presidency, Reagan has stepped up the number of his daily appearances, abandoning the leisurely pace that had for weeks been a trademark of his campaign -- the late morning baggage calls, and even the institution of a morning laundry call before departure, a luxury unknown to campaigns past.

Carter's campaign, meanwhile, remains at its normally franctic pace.

After shoring up his southern base this weekend, Carter will conclude his campaign on Reagan's western turf.

On Monday, after campaigning in the Midwest, Carter is scheduled to fly to Los Angeles for a suburban rally; and then to Portland, Ore.; and Seattle, Wash.; and finally back east through the predawn hours of Election Day in time to vote in Plains, Ga.

This Monday schedule has provoked considerable interest within the Reagan high command. Carter officials have talked optimistically about how they have closed to within six points of Reagan in California, but Reagan officials insist their lead in this biggest of states is larger than that and in fact is increasing.

Since electoral votes in each state are awarded on a winner-take-all proposition, there is no point to making a heroic and costly effort just to finish a closer second; and so, Reagan's senior strategist and pollster Richard Wirthlin found himself asking yesterday: "Is that Monday schedule just a bluff? Is Carter really going out to California on the last day?"

Carter officials swear that the schedule is for real -- but the trip out West appears to be aimed more at Oregon and Washington than at California alone. For the races in both states in Reagan's western base are said to have closed significantly, even in Reagan's own polls.

For all the attention that has been focused upon the big northern industrial states, victory in this apparently close national election may hinge on the question of which candidate is best able to secure his own base from defeat.