The problems with the ad are plentiful, and The Anchoress does a nice job of pointing them out. She also points out that the ad is likely effective anyway - as Craig Westover likes to note, when it comes to politics bullsh*t often is.
But really, one of the main problems here isn't with the ad itself. It's with the way political leaders on the pro-life side have dropped the ball (again) when it comes to explaining the fundamentals of their opposition to a public being saturated with misinformation by embryonic stem cell research proponents.
To understand that opposition you need only grasp some very elemental points of ethics. Deep understanding of the scientific data is not required, because the opposition isn't based on some technical detail subject to empirical discovery. The opposing case is very simply this:
A. It is wrong to kill innocent human beings for the medical benefit of other human beings.
B. Human embryos are human beings.
That's it. Every argument flowing out of opposition to embryonic stem cell research logically procedes from there.
The issue is obviously extra heated because of that "embryos are human beings" proposition. Not even all those opposed to abortion go that far. Embryos are, after all, a VERY early stage of human development.
And yet I find that position entirely defensible. Embryos are - speaking in terms of pure science - individual members of the species homo sapiens at an early stage of development. If you decide to assign them some kind of "less than fully human" status, you certainly can. But in doing so you are implicitly embracing the notion that humans may arbitrarily decide which human lives they are bound to respect, and which they may conveniently ignore. Even if you personally don't agree that embryos are "fully human" you might take caution about endorsing that proposition, because not everyone will stop at "embryos." Indeed, history suggests a very real slippery slope on the other side of that line.
This was one of the main themes of the late Pope John Paul II when he spoke about a "Culture of Life," and "Culture of Death." The most vulnerable human lives - from voiceless, defenseless embryos, to the old and infirmed, to the chronically ill, to the mentally incapacitated, to those deemed "useless" - are most at risk when people start entertaining arguments about which human lives they are bound to respect. Aw, heck. He said it better than I can:
Another area in which political and moral choices have the gravest consequences for the future of civilization concerns the most fundamental of human rights, the right to life itself. Experience is already showing how a tragic coarsening of consciences accompanies the assault on innocent human life in the womb, leading to accommodation and acquiescence in the face of other related evils such as euthanasia, infanticide and, most recently, proposals for the creation for research purposes of human embryos, destined to destruction in the process.
A free and virtuous society, which America aspires to be, must reject practices that devalue and violate human life at any stage from conception until natural death. In defending the right to life, in law and through a vibrant culture of life, America can show the world the path to a truly humane future in which man remains the master, not the product, of his technology.
While extending the "human" line to the embryo seems extreme to some, it's only so because the line is set in principle rather than convenience or utilitarianism.
Opposition to embryonic stem cell research requires no more than the acceptance of a clear and simple ethic. Supporting embryonic stem cell research rests upon deformed and unpredictable ethics, fueled by increasingly dubious scientific hope.
I like to think about it like this... Whether the scientific benefit of extracting stem cells from human embryos is real and certain, or concretely impossible, my position on the issue is the same. If you support embryonic stem cell research and you KNEW it would never produce a viable cure for people like Michael J. Fox (or anyone else) would your position also remain the same? If not, how is that anything other than utilitarian formulation? And is utilitarianism ever a good way of determining a human being's right to life?

Where do they generally get the embryos for these sorts of research?
Here's a medical article to dig through that seems to answer your questions. It's a pdf.
OK. So on the one hand, they can do some of this research with adult stem cells which pretty much everyone is cool with but may not have the potential of embryonic stem cells.
On the other hand they can do research with stem cells harvested from embryos that are at 5 - 7 days post-conception. These cells seem to have the most potential (pluripotent) stem cells and scientists believe that there is more that can be done with them, but it "requires the disaggregation of the early embryo - hence the ethical debate". Parse that, eh?
Unfortunately, it still doesn't say where they get these embryos for, er, "disaggregation". I can see how to some people that doesn't make a difference because "they're all bad", but I see an ethical difference between:In the first case I outlined, I've got to admit, I'm having a hard time seeing a problem with. I really do understand how someone would scientifically or religiously define this as a human life but it just doesn't fit my gut check as being a human being. I mean, did you see the pictures in that article of what 5-7 days after conception looks like? And if this conception takes place in a petri dish in a lab rather than in a human body? I dunno, it just doesn't register at any level as human to me.
That said, I really do get your slippery slope concern. I can see it leading to (assuming the technology gets there) lab cloning of fully developed adults who are kept comatose from birth and used as organ donors for their progenitor. Sci fi is great for exploring ethical questions like this and there is a clear slope from a cloned 5-7 day embryo to a some very nasty places.
In any case, do I think federal money should be spent on this? Fuck no. Federal money shouldn't be spent on a 1,000th of the stuff its spent on. The federal government should take care of international treaties and trade, border defense, interstate commerce and multi-state concerns, post, and being a judiciary of last resort. Just like the constitution says. All this other stuff should be done on the state or local levels or not at all. All of it. There's a slippery slope we've fallen down so far and fast I don't know when we're going to hit bottom. Incidentally, I DO think the feds should realize that the net is a modern extension of the post.
Do I think a state might choose to do this sort of research? Well, yeah, if they stay on the top end of the slippery slope and are really careful and deliberate about taking any step which could cause them to slip. Lots of talk before any action. Of course, if they do start slipping they may quickly get to the point where they're clearly violating the rights of a human being and then its the fed's job to say "NO".
I think it would be wise to have a federally defined point at which human rights are recognized. My gut says that it should be roughly at the point where the brain develops enough to have basic functions but again I do recognize that reasonable people can and will disagree on this. The 14th amendment implies birth, but they're talking about rights of citizenship rather than basic human rights.
Too bad it always ends up being so polarized. I've got to think that a lot of people who are pro-life aren't really in it because they don't want to let women have control over their own bodies. I've also got to think that a lot of people who are pro-choice aren't really in it because they have no respect for human life. Even the names carry with them the implication that the other side is "anti-life" or "anti-choice". And both sides are scared of the slippery slope. Try defining when an unborn baby gets its rights and you'll hear a lot of slippery slope concerns.