Guest host John Dickerson asked Dan Balz, columnist for the Washington Post, why.
"In 2004 the Republicans needed to do everything they could to motivate their base," Balz said. "Their base this year is highly motivated. They don't need to do more to crank up the anger.
"The second (and I think more important) reason is they have very good issues to deal with in this midterm [election]: The economy, the size and scope of government, and the deficit. Those are issues that unify their entire coalition and also reach out to independents.
"To introduce, in a significant and loud way, same-sex marriage, would threaten to pull that coalition apart," he said.
Dickerson also asked Tony Perkins, the head of the conservative group Family Research Council, why the Republican response has been rather muted.
Perkins, besides promising that the fight is "far from over," said there will be a resolution in Congress on the matter in the coming week when the House of Representatives reconvenes.
CBS News chief legal correspondent Jan Crawford noted that the Democrats are equally conflicted and quiet in their response.
"While much of the Democratic base favors same sex marriage, the truth is most elected officials (including President Obama) are opposed to it. So there is conflict within their base," Crawford said. "They don't want to really get into this at this point and stir things up. The president has stayed away from this issue for the most part, as have most other Democrats.
"So I don't think you're going to see Democrats try to leap to make this into an issue in the fall."
She added that while same-sex marriage may not become an issue in the fall 2010 elections, but it will become prominent in two years' time.
"This case is going to get to the Supreme Court pretty close to 2012," Crawford said. "Whether or not it's an issue in this year's midterm or not, it's going to be an issue in the presidential election."
"Public opinion is changing on this, fairly dramatically over the last four or five years," Balz added. "But it's not at the point where there's majority opinion in a majority of the states in favor of same-sex marriage. The court may end up ruling on this long before public opinion reaches the conclusion that a majority favors same-sex marriage."