No one doubts that Sen. John Sununu has a fight on his hands when he runs for re-election next year. But if former governor Jeanne Shaheen decides to challenge Sununu to a rematch, a new poll shows he could face a rout.

A new Monitor poll has Shaheen, a Democrat, handily beating Sununu, a Republican, 56 percent to 34 percent. But paired against any of the Democrats currently in the race to unseat him, Sununu wins, holding a 46 percent share while the challengers' support ranges from 24 to 32 percent.

"It's whether Shaheen wants to make him a present by staying out of the race," said Linda Fowler, a Dartmouth professor of government. "If she doesn't, he might squeak by."

Nine months after Granite Staters voted Democratic up and down the ballot - giving the party control of the House, Senate, governor's office, Executive Council and both congressional seats - the climate remains hostile to Republicans.

Perhaps the single clearest expression of New Hampshire's state of mind: A majority of the 600 likely voters polled last week said they would support impeachment proceedings against Vice President Dick Cheney, with 52 percent in favor and 38 percent against. President Bush narrowly escapes that category, with 43 percent supporting impeachment action and 45 percent opposed.

At the moment, Democrats in the race to challenge Sununu are Katrina Swett of Bow, Dartmouth Medical professor Jay Buckey and Portsmouth Mayor Steve Marchand.

But many Democrats are pulling hard for Shaheen to join the contest against Sununu, who in 2002 narrowly beat her in the race for that seat, 51 to 47. Former Democratic Party chairwoman Kathy Sullivan has launched a Draft Shaheen committee, which boasts a staffer, a website and support from some high-profile Democrats, such as Sen. Peter Burling.

Shaheen has said she's mulling a run but has not decided or said when she'll make up her mind.

The poll, conducted this week for the Monitor by Research 2000, also found that Sununu's favorability ratings have sagged while Shaheen's have held steady since 2002. The poll has a margin of error of plus or minus four percent.

In October 2002, when Sununu was in a tight Senate race against Shaheen, voters liked them both: He had a favorability rating of 56 percent; hers was 58 percent. Now, after Sununu has served most of a term in the Senate and Shaheen has taken the helm at Harvard's Institute of Politics, his favorability rating ranks at 43 percent, while hers stands at 55 percent.

The Monitor poll on the Senate race is in line with two polls from last month. A Suffolk University poll had 31 percent of likely voters saying Sununu deserves to be re-elected. And an American Research Group poll of registered voters had Shaheen beating Sununu, 57 percent to 29 percent.

While Shaheen appears to be the one to beat in this race, Sununu should be worried about the head-to-head matchups with lesser-known candidates Swett, Buckey and Marchand, pollster Del Ali said.

With Sununu holding steady at 46 percent, Swett takes 32, Marchand 29 and Buckey 24 percent. (For good measure, the Monitor also pitted Sununu against Rep. Paul Hodes, a first-term Democrat whose interest in the seat has been the subject of rumors. In the poll, Hodes takes 34 percent to Sununu's 46 percent.)

Ali said that if he was one of the lesser-known Democrats in the race, he would be touting these poll numbers to donors. The selling point of those talks would be: "I'm an unknown, and he can't garner 50 percent."

Democratic Party Chairman Ray Buckley agreed.

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