Any issue involving gay people
Democrats cannot talk about taxes because every proposal ends with an increase in taxes. They decry the Republican tax cuts and use the common refrain of the need to "invest" in various programs. There is groundswell in the blogosphere for supporting a reduction in pork spending. Many people are calling for the elimination of earmarks all together while other believe we should simply add transparency as the old saying goes; "sunlight is the best disinfectant." Given that members of Congress use earmarks to get themselves re-elected it's inevitable that they will not be able to restrain themselves in spending. The best policy is to eliminate the use of earmarks altogether. Further, I would like to see a bill past that prohibits adding any riders to a bill that are not directly related to that bill. This would prevent the highway and defense bills from becoming the kitchen sink of legislation where most of the pork is buried. The President proposed a line-item veto which is remarkable only because I didn't think he was even aware he had the power of veto. He also knows it's pipe dream and one he can use as a club to beat the Democrats with later. "When buying and selling is controlled by the legislature, the first thing bought and sold are the legislators" as P.J. O'Rourke once remarked. The only way to defeat every increasing taxes is to decrease the size of government by restraining the funds they have available. Apart from repealing the 16th Amendment (http://en.wikipedia.org/wiki/Sixteenth_Amendment_to_the_United_States_Constitution), I can't see a practical way to decrease the size of government.
Similarly, national security has become a verboten topic. Any attempt to be hawkish in the Lieberman mold results in a deluge of vitriol from the Kos Kids and any attempt to appease them by advocating a cut and run strategy alienates everybody else. It is inevitable that Republicans will seize this ground and make it central to their campaign. Their response to the domestic and "warrantless" wiretap programs are not running from the issue but plan to embrace it. That means either they are on rock solid legal ground or they believe they know that John Q. Public strongly supports such a program. I suspect the latter is more likely than the former.
Republicans are unable to face the issue of gays in America. As Andrew Sullivan notes, Bush has yet to mention the words gay or homosexual since taking office. It's weird and almost as if he can't bring himself to say it. I believe most Republicans know that gay people aren't going anywhere and they're not going back in the closet (nor should they) and in the end, they're just like everybody else. However, they can't say that for fear of the inevitable apoplectic outrage that would come from the Evangelical community.
Government has never been bigger. It now consumes more time and money than ever before. It impacts every aspect of your life and it is inescapable. Extraconstitutional spending has been rife for decades and it's not going anywhere. Republicans have basically turned their backs on Reagan and Goldwater and become the party of Big Government. Their logic (if you can call it that) is, government is going to be big and this money is going to be spent so we might as well be the ones doing the spending. They'll never admit that because they would alienate most of their base. We all know it but we turn a blind eye because the idea of John Kerry or Hillary Clinton in the White House is far more to bear than government spending.
Everybody avoids pork spending for the reasons detailed above. There is an enormous amount of money flowing into Washington and the piggies know they are fighting for pieces of the same pie. They are all too anxious to get federal dollars to put their name on something, anything, that shows they know how to bring home the bacon. Robert Byrd is the most pervasive example while Ted Stevens' "bridge to nowhere" is the most egregious.
Immigration reform is a non-starter. The President wants an amnesty program cloaked as some other name while the rest of his party says no. In truth, Republicans cannot put up a wall to block of Mexico because the Small Business Administration lobby would kill them. They need the cheap labor to keep them in business. Without illegal labor, a great many of people would be mowing their own lawns. Democrats will not go for anything other than amnesty as it's the surest way to increase their voting base. I think a great many Americans believe in immigration but think we ought to be in control of it and find out exactly who is crossing our borders.
Abortion is one debate neither side wants settled. Both sides know a great deal of their base is motivated by abortion. Kicking this issue back to the states where it belongs would require both sides to come up with another touchstone issue that would exite their voters enough to get to the poll. How many people would sit home on election day if they knew the abortion issue was removed from the equation?