Even though Thompson has a 100% pro-life voting record and has been endorsed in the past by National Right to Life, apparently that isn’t good enough:

Imminent 2008 presidential candidate Fred Thompson is positioning himself as a new hope for social conservatives who are unhappy with the current field of 10 Republicans.
But his answers on past surveys indicate he has previously taken positions that could be viewed as tolerating abortion.
Documents The Tennessean located last week in Thompson’s Senate archive at the University of Tennessee show:
– On a 1996 Christian Coalition survey, he checked “opposed” to an amendment to the U.S. Constitution “protecting the sanctity of human life.”
– He included a handwritten clarification: “I do not believe abortion should be criminalized. This battle will be won in the hearts and souls of the American people.”
– In 1996, asked by the Memphis group FLARE (Family, Life, America, Responsible Education Under God Inc.) if human life begins at conception, Thompson circled “N/A.”
Those answers could complicate Thompson’s standing with the Republican Party right wing, which has been bolstered by his seemingly reliable pro-life voting record.
Thompson and his small campaign staff say he has never supported abortion rights.

This appears to be the stick in which the left and right are poised to hit him over the head. The left can say, “He’s not conservative enough maybe you social conservatives need a Gingrich or a Brownback,” knowing that they would have little appeal to moderates. And the right will say, “He’s not pure enough for us” in an attempt to nominate a candidate who meets their standards.
But if conservatives don’t coalesce around a candidate, then we will split our vote and Giuliani has a chance of winning the primary and we will only have ourselves to blame.
Updated: I published this by accident the first time. I had some thoughts along the lines that this would be a good way for the media to hit Thompson from the right but I didn’t like the way it was coming out and it was time for me to leave for church, so I just saved it and didn’t realize I had published it!