By Michael Duffy, TIME

With less than a week of campaigning left, Democrat Barack Obama is holding stable or growing leads over Republican John McCain in Nevada, North Carolina and Ohio, according to a new set of TIME/CNN battleground-state polls conducted by Opinion Research Corp.

Obama leads McCain among likely voters by 51% to 47% in Ohio, a 4-point margin that has not budged since last week’s TIME’s survey. But he now leads McCain by 52% to 45% in Nevada and by 52% to 46% in North Carolina, margins which are both slightly larger than those reported by TIME in its surveys a week earlier.

The new statewide surveys also show Obama leading McCain in Pennsylvania, the key blue state in which McCain is making a last-ditch, major push to score an upset, by a comfortable 12-point margin of 55% to 43%. But Obama still trails his Republican rival in McCain’s home state of Arizona by a 7-point margin of 46% to 53%.

Clinging to a narrow lead in Ohio, perhaps the most closely contested state in the nation, Obama continues to perform best with women of all races, who back him over McCain by a narrow but crucial 55% to 43% margin, a slight improvement from a week before.

But while Obama’s performance among women in Ohio was firming, his support among men was weakening. Men in Ohio now favor McCain and Sarah Palin over Obama and Joe Biden by a margin of 51% to 47%, compared to a gap of 49% to 47% a week before.

Among Ohio’s white males, meanwhile, Obama appears to be falling faster: they now favor McCain by a 14-point margin of 56% to 42%. Just a week earlier, Obama was 10 points behind with this group. Joe “the Plumber” Wurzelbacher, who has come to represent something like a mascot or a rallying cry for the McCain campaign, hails from a suburb of Toledo, Ohio.

White men in Pennsylvania, by comparison, favor McCain too, but by a narrower 50%-46% margin, the TIME/CNN poll found. Women in Pennsylvania are more comfortable with the Democratic nominee than their counterparts in the Buckeye State to the west, though the difference is less dramatic. Keystone State women back Obama by a margin of 57% to 42%.

But the differences among key groups in Ohio and Pennsylvania are minor when compared with the demographic breakdowns in North Carolina. Though Obama leads in North Carolina by 6 points overall, McCain leads Obama among white women by an overwhelming margin of 62% to 32%, a ratio that is virtually identical to the margin reported by white men, who favor McCain 64% to 34%.

In Nevada, by contrast, Obama has seen his lead overall grow from a 4-point margin in late August to a 7-point margin in the latest TIME/CNN poll. Most of that growth, the data shows, comes from independents, white men and voters making less than $50,000 a year. McCain’s overall support in the state — 45% – is only 1 point higher than it was two months ago.

The polls were conducted over the phone from Oct. 23-28. In Arizona, 807 likely voters were surveyed; in Nevada, 684; in North Carolina, 667; in Ohio, 779; and in Pennsylvania, 768. Arizona, Ohio and Pennsylvania had a margin of error of plus or minus 3.5 percentage points, while Nevada and North Carolina had a margin of 4 percentage points.