Its hard to say what the reaction will be. Mills has the added problem of disloyalty. He all but refused to endorse Woodcock in the general, and many of his leading supporters backed Merrill. He also has problems with some people around Snowe, and one reason he lost the primary is that she recruited former congressman and general has-been David Emery into the primary against him.
I remember there being a Republican "unity" event shortly after the 2006 primary with Peter Mills and Dave Emery each pledging their support for Woodcock. I think a lot of Republicans felt and still feel, though, that Peter Mills hurt Woodcock's campaign by openly opposing the Taxpayer Bill of Rights proposal on the ballot that November, which Woodcock, Emery* and the state Republican platform supported and which Woodcock tried to make a major part of his campaign. Like a lot of citizen initiatives supported by those who participate in politics most noticably in circulating petitions (conservatives mostly, with a major exception on land use issues where sportman's advocates make nice with the Democrats and hold significant sway in the Legislature and the Governor's office) and opposed by those who participate in politics cheifly in getting like-minded people elected and warning/lying to people (depending on your point of view) about what will happen if the citizen initiative in question passes, TABOR tanked in October, and Woodcock's numbers dropped a bit although Baldacci's did as well, with Barbara Merrill being the big gainer although she was still a distant third which is how she finished.
Some vocal conservative activists who frequent the conservative web site
As Maine Goes seemed to direct a lot of their anger for TABOR's defeat at Mills, although I didn't see him in any anti-TABOR (let alone anti-Woodcock) commercials. A self-described "lifelong Republican" former state Representative, Sherry Huber, who nonetheless had run for Governor as an Independent in 1986 after losing the Republican primary in 1982 starred in a biting ad against the Republican nominee, detailing Woodcock's social conservative stands and ending by saying, "I'm a lifelong Republican, but Chandler Woodcock is out of touch with Maine people." Many on AMG equate Mills's actions with Huber's, although I think they're very different. Of course, in politics, perception is more important than reality, and in the perception of conservative Republican activists Mills betrayed his party in 2006 after losing the primary.
*A moderate Republican activist/sometimes legal council, although he supported Woodcock in the primary, said that Woodcock was the clear 2nd choice of the majority of Emery voters, although the general perception of those who lightly follow politics is that Woodcock only won the primary because of the split in the moderate vote and that Mills would have beaten Woodcock in a 2-candidate primary.
Well then he better have a good relationship with the Collin's people then. My suggestion to him would be to make peace with Snowe and try and unite the Moderate GOP vote.
I've heard Mills being associated with the "Collins wing" of the Maine Republican party, which would show how personal the divide between the Collins and Snowe wings are as Collins is a bit more loyal a Republican vote than Snowe while Mills is probably by most standards the least reliable Republican vote among Republicans in in the State Senate (I'm not sure about the overall legislature). There may be a bit of a costal (Snowe faction: Charlie Summers, Dave Emery, Kevin Raye (of Washington County)) v. inland (Susan Collins (from Aroostook County and living in Caribou last I knew when she's not in Washington, although she lived in Cumberland County when she ran for Governor in 1994), former Bangor Mayor and 2002 Congressional candidate Timothy Woodcock, 1994 Congressional nominee and former State Senate President Rick Bennett of Oxford County, and Peter Mills of Somerset County) divide among non-social conservatives in the Maine GOP.