A new batch of polls over the last three days shows Hillary Clinton still in a dead heat with Barack Obama in the first-to-vote Iowa caucuses on Jan. 3, but regaining her footing in the first full-fledged primary in New Hampshire on Jan. 8.

As for the other early-voting state, South Carolina, the most recent poll has Mike Huckabee tied with Mitt Romney.

Looking further down the road, Clinton still holds double-digit but declining leads over Obama in big states like Florida and California. On the Republican side, Rudy Giuliani still in California, but Huckabee has closed the gap from 21 points to eight points in the last six weeks.

In Iowa, the Washington Post-ABC News poll conducted Dec. 13-17 put Obama ahead of Clinton by 33 percent to 29 percent, a difference equal to the survey’s 4 point margin of error. John Edwards is at 20 percent with everyone else in single digits.

However, in New Hampshire, where Clinton’s “firewall” against the prospect of an Iowa loss appeared to be cracking, she may have regained some of her footing. A CNN/WMUR-TV poll on Dec. 12 had Clinton in a statistical tie with Obama. But a new CNN/WMUR survey released today had Clinton in the lead 38 percent to 26 percent with Edwards at 14 percent. The caveat on this poll is that New Hampshire voters historically make up their minds late and 38 percent said they had not definitely decided for whom to vote.

A separate poll by Rasmussen Reports also finds a change in Clinton’s favor in New Hampshire with her picking up 6 points to lead Obama 31 percent to 28 percent.

But perhaps a bigger development on the Republican side is the rising numbers of John McCain, fresh off his endorsements by the Manchester Union Leader and Boston Globe. Prior to those endorsements, Romney led McCain 33 percent to 18 percent. The latest survey shows the race tightening with Romney still at 33 percent, but McCain up to 27 percent.

In South Carolina, Rasmussen Reports released a Republicans poll on Monday that had Huckabee and Romney tied at 23 percent, followed by John McCain and Fred Thompson tied at 12 percent. In that race too, the pollsters warned that the voters’ choices were very fluid.

A new Field Poll in California reported that Clinton’s lead over Obama – once 25 points – has now fallen to a 36 percent to 22% margin. Edwards is in third with 13 percent and the others are in single digits. However, California Democrats see Clinton as more electable than Obama in November by a wide 52 percent to 18 percent margin. If Edwards were to drop out before California, the survey indicates his backers would be more inclined to support Obama. The number of Democratic voters who say they are undecided grew from 14 percent in October to 20 percent.

A separate SurveyUSA poll of California also showed Obama cutting into a Clinton lead it had put at 37 points two months ago. Now, Clinton leads Obama by a still considerable, but lesser, 49 percent to 30 percent. Among Republicans, Giuliani’s lead was once 21 points over his nearest rival; now he is ahead of Huckabee by only 28 percent to 20 percent.

In Florida, Huckabee has closed to five points of Giuliani, trailing by 29 percent to 24 percent.

As for the horse-race nationally, USA Today/Gallup reported Tuesday that Huckabee’s surge had leveled off and Giuliani led with 27 percent, followed by Huckabee’s 16 percent, and McCain, Thompson and Romney tied at 14 percent. Clinton led Obama 45 percent to 27 percent with 15 percent for Edwards.

A Diageo-Hotline poll, also released Tuesday, showed no clear favorite in either party in a “national primary.”

There were a number of national and state polls that matched-up the leading Democratic contenders against the Republican leaders.

Gallup found in a poll released today that Obama does as well as or better than Clinton against Giuliani, Romney and Huckabee while Giuliani does better than his rivals against Clinton or Obama.

On a regional scale, a series of polls by SurveyUSA in four heartland states -Minnesota, Wisconsin, Ohio and Missouri – generally showed that Clinton won in match-ups against the top GOP candidates more than Obama and, on the Republican side, the top tier Republican who fared the worst in each state was Romney.