President Carter now holds a commanding 58-38 percent lead among Democratic voters over Sen. Edward M. Kennedy in the race for that party's nomination.

But there is even better political news for the president. A 66 to 29 percent majority of all voters feels that "after a bad start, he now seems to have caught hold of the job and it looks like he'll do a good job." This is a marked improvement from the 53 to 41 percent majority who shared that view in late November and the 51 to 40 percent majority of July.

The swing toward Carter can be seen among almost every group: in every region, among every age group, at all levels of education, among men and women, and in every income and occupational group. Carter is ahead among all these key segments of the Democratic electorate.

There are three exceptions to the Carter lead:

Among black Democratic voters, Kennedy clings to a 49 to 45 percent lead. But the senator had a 5-to-1 lead in July, and a 2-to-1 lead in late November.

Among Jewish Democratic voters, Kennedy holds a 52 to 44 percent lead, but this is far from his 3-to-1 lead in early November.

Among Democratic liberal voters, Kennedy is ahead by the narrowest of margins, 49 to 48 percent, down from the 2-to-1 lead the senator held in early November, and from the 3-to-1 majority he enjoyed among liberal Democratic and independent voters in July.

The survey was conducted between Dec. 14 and 16 among 910 likely Democratic voters.