But judging by some recent statements, Giuliani isn't exactly trying to soothe conservative concerns. On TV and during a swing through the early primary state of South Carolina, Giuliani has for public financing of abortions for women who cannot afford them.
"Ultimately I believe it's an individual right, and a woman should make that choice," he said.
Republicans' views on abortion are not uniform. Some want them banned outright, some want to allow it only in cases of rape and incest and others favor full abortion rights. But, in a party that views public funding of even non-controversial medical procedures with skepticism, putting taxpayer money toward abortions is pretty much off the table.
In the past, Giuliani has tried to temper his stance somewhat by saying he believes states should decide on public funding, not Congress. He has also claimed that, if given the chance to nominate someone to the Supreme Court, he would pick a strict constructionist in the mold of Antonin Scalia or Clarence Thomas — both of whom have criticized the court's 1977 ruling in Roe v. Wade that legalized abortion nationwide.
Christian conservatives might see this as nothing more than sugar-coating in light of his latest pronouncements. To them, abortion is a moral issue, not a legal one. Allowing it, much less funding it, in one state is as bad as doing so in any other.
So far at least, Giuliani's approach hasn't seemed to hurt him in the polls or on the fundraising front. Emphasizing his views on national security and his role as New York mayor during 9/11 have been the signatures of his campaign. A greater emphasis on his socially liberal views, however, could lead to tumult in the polls — and leave an opening for anyone waiting in the wings, like former House Speaker Newt Gingrich or former Sen. Fred Thompson.
Democrat Debate-A-Thon '07: The Democratic National Committee announced Thursday that it would sanction six debates between its presidential candidates. The debates would start in July and be held monthly until December.
Representatives of Hillary Clinton, Barack Obama and John Edwards reportedly had lobbied the DNC to limit the number of debates. Why? Front-runners don't like them because they have little to gain from them, while dark horse candidates with nothing to lose can get a bounce out of a good performance. Debate prep also takes time away from controlled solo appearances and fundraising.
The DNC's decision doesn't stop every TV station and newspaper in Iowa and New Hampshire from sponsoring a debate. But those without the DNC's seal of approval might have a harder time getting top-tier candidates to attend.
New Hampshire's New Controversy: Democratic candidates in South Carolina have long had to tip-toe around the state's decision to fly the Confederate battle flag above its state capitol, which some African Americans see as an offensive reminder of slavery. Now, New Hampshire might have its own parochial pitfall: gay marriage.
The state's House of Representatives voted on Wednesday to pass a bill that would create civil unions for same-sex couples. The state Senate is expected to pass the bill, but Democratic Gov. John Lynch, who says he opposes gay marriage, has not indicated whether he will sign the legislation.
Normally the diciest question candidates in New Hampshire have to deal with is whether they support the state's effort to maintain its first-in-the-nation primary. Of course, they all say yes to a question no one outside of New Hampshire really cares about. But being asked about civil unions introduces a more uncomfortable issue.
While Republican primary voters by and large oppose gay marriage, there is slightly more wiggle room on civil unions, which don't carry a religious connotation. Still, expressing support for such unions is a risky proposition. Even if New Hampshire Republicans don't mind them, conservatives in other states may be strongly opposed.
The good news for Democrats is that full-blown gay marriage isn't under consideration — the difference between a civil union and a marriage is largely semantic, yet supporting the former while opposing the latter is the middle ground on which most Democrats have settled.
HPV Veto: If you thought the New Mexico legislature wrapped up its session by sending Democratic Gov. Bill Richardson only softball legislation on cockfights and bolo ties, you'd be wrong: Legislators also passed a bill requiring all girls entering sixth grade to be vaccinated against human papillomavirus.
Similar legislation created a controversy in Texas, where it was signed into law by conservative Republican Gov. Rick Perry. So it might come as a surprise that Richardson, a left-of-center Democrat in a moderate state, vetoed the measure. "While everyone recognizes the benefits of this vaccine, there is insufficient time to educate parents, schools and health care providers," he said in a statement.
Richardson's response is a sign that the controversy over mandating the vaccination isn't purely partisan. While those who believe the vaccine could promote sexually promiscuous behavior in teenage girls might make up a large chunk of the opposition, they have been joined by those who oppose mandating the treatment out of distrust of large pharmaceutical companies. Other opponents include parents who simply don't like being told what to do and people who are concerned about the possible side effects of such medications.
When the partisan divide over an issue is this muddled, it makes it safer for a governor, even one running for president like Richardson, to make a decision without fear of angering supporters beyond repair.
Keep Those Lessons Coming: While Gingrich may be seen as a savior-in-waiting by some conservatives, he hasn't done himself any favors this week with Latino voters, a group the GOP has been courting since President Bush's first run in 2000.
Gingrich has issued a YouTube apology for a speech he delivered on Saturday in which he equated bilingual education with "the language of living in the ghetto" — a remark that immediately drew fire from bilingual education advocates and Latino organizations.
In his video apology, delivered Thursday in Spanish with English subtitles, Gingrich said, "I have never believed that Spanish is a language of people of low income not a language without beauty." He also says that he has been taking Spanish lessons and admits that his Spanish "is not perfect."
His skill with the language is pretty apparent from watching the video. While his words are letter-for-letter perfect, Gingrich's accent is pretty nonexistent and pales when compared to the Spanish spoken by President Bush and his brother, former Florida Gov. Jeb Bush.
Of course, Gingrich says he won't decide whether he'll enter the presidential race until September. He can probably work in plenty of Berlitz classes until then.
Editor's Note: Pure Horserace is a daily update of political news as interpreted by the political observers at CBSNews.com. Click here to sign up for the e-mail version, coming soon to an in-box near you.
By David Miller