Just as important as the recent findings that President Carter would run behind Gerald R. Ford if a rematch of the 1976 election were held today is another item of critical information:

In the judgment of voters, the president is rated no better than 61 to 34 percent negative on "inspiring confidence in the White House."

Throught the years, the Harris Survey has found this to be a key rating in predicting the near-term fortunes of the occupant of the White House. As recently as last December, a 55-to-39 percent majority still thought that the president "inspired confidence in the White House."

His overall job rating may have been dropping into the negative column, but the publci refuse to lose faith in his capacity to inspire them. Even in January, while his overall rating turned more negative, his personal confidence standing remained 50 to 44 percent positive.

Now, in the latest survey of 1,498 voters, the president's overall job rating has gained 7 points, reflecting his successes on the Panama Canal treating and the sale planes in the Middle East.

But, at the same time, his personal confidence rating has continued to slip, going from 50-to-35 percent negative in April to 61-to-34 percent negative in May.

The details of this shift are even more discouraging for Carter. Among the voters who cast their ballots for him in November 1976, a 50-to-45 percent plurality now gives him low marks on his ability to inspire confidence. Among the rank and file of Democrats, a 51-to-43 percent majority shares this assessment . And, in his own home region of the South, an even higher 58-to-37 percent majority no longer thinks he inspires confidence.