-Personhood-
First off I would like to emphasize that I'm arguing personhood and not life here. If we are to argue life then we should start with sperm, at which point it would mean that even if a child is ultimately produced or not millions are dying.
Let's start with where we are in development. What you're seeing here is a fetus at ten weeks of gestation.

All basic structures of a human are present but not fully formed. The heart has been beating for about 4 weeks at this point (not controlled by the brain but by a rudimentary nervous system.) No brain wave activity is yet present. The fetus is likely under 2 inches in length. (A fetus at 13 weeks is usually about 2 inches long.)
Most abortions take place before this point of development is reached. At around a week or two (8-9 weeks gestation) before the point illustrated above, it can usually be determined if the fetus is viable or not to be carried to term. This is why most abortions take place at the 8-9 week stage. As many are not viable, thus could not survive to term and/or could cost the mother her own life if carried to term.

This point is also well before rudimentary brains waves can be detected which occur around 26 weeks.
"26 weeks or 6 months: The fetus 14" long and almost two pounds. The lungs' bronchioles develop. Interlinking of the brain's neurons begins. The higher functions of the fetal brain turn on for the first time. Some rudimentary brain waves indicating consciousness can be detected. The fetus will probably be able to feel pain for the first time. It has become conscious of its surroundings. The fetus has become a sentient human life for the first time." -Pediatrics, Wisconsin State University
Considering a basic etiological definition of personhood would require consciousness over a period of time. Something that the fetus has not yet developed in the span that most abortions take place. Or another way to put it ;"the state or fact of being an individual or having human characteristics and feelings" -Dictionary.com
This is something the fetus clearly lacks.
The argument of being human starting at conception can be supported by the argument that the individual cells making up the zygote are genetically different from that of the parent. While this may indicate a separate organism, this does not indicate personhood. If we wish to argue that just being a separate organism dependent on the larger organism to survive is a person, then we are left arguing many aspects of individual parts of the human body should be regarded as separate people. This particular grouping unlike those other parts however has the potential to develop into a person. But potential alone can be ruled out as we do with sperm.
Since it was brought up the point at which the fetus has a heart beat doesn't seem like a good point to consider it a person either. This occurs around 6 weeks gestation. The fetus lacks self sustaining viability and even lack basic brain waves. If we are to just go by it having a heart beat, there are many living organisms with heart beat that are not consider to have personhood.
The argument that we are killing babies really often comes off as nothing more than an emotional plea. We aren't dealing with the imagery that is being conjured up in such a statement.
We aren't dealing with this.

But something closer to this.

(One is a human fetus the other is not, care to figure out which you are calling a person and which you are not?)
To sum it up in simple terms I will quote 314d1.
"Sperm= Potential human
Egg= Potential human
Fetus= Potential human
None have a brain enough to be able to think, feel pain, or anything that will make them a person... If it is taking away potential life that is wrong, then warring condoms is also wrong or even just not having sex." -314d1
-The costs and rights-
The argument against abortion often ignores the rights of the mother. We do have to consider that any such rights to the developing fetus has a direct affect on the mother.
"Until the fetus is viable, any rights granted to it may come at the expense of the pregnant woman, simply because the fetus cannot survive except within the woman's body. Upon viability, the pregnancy can be terminated, as by a c-section or induced labor, with the fetus surviving to become a newborn infant." -wiki
When considering human rights applied to a fetus, at what point do we consider the rights of the woman who will be forced to carry the fetus to term?
Another thing to consider is that adoption services are already over crowded. "Out of 4,242 foster homes, 16% of foster homes are over their licensed capacity even though 52% of foster homes are under their licensed capacity. There are currently 62 foster homes with more than 10 children." -source
To make abortion illegal would cause an influx to this system of over a million children a year. This could have an impact on the over all quality of life for those in such a system and would cost millions a year more in taxes to support. This isn't even getting into the resource demands as they grow up or the ones who stand no chance at a normal life due to severe mental and physical problems.
On the point of if abortion is right or not I would like to quote Moegreche from a earlier thread on this topic.
"No one actually thinks abortion is the "right" thing to do
Instead, here's how we need to think of the 2 extremes:
Pro-Life (PL): Abortion is never morally permissible, therefore abortions should not be allowed to be performed legally.
Pro-Choice (PC): There are cases in which abortion is morally permissible, thus abortions should remain legal.
Notice that PC here is not suggesting that abortions are the morally correct choice - only that there are situations in which a mother who gets an abortion should not be morally blamed.
There are some within the PC camp who say that a mother should be able to do with her body what she will, and that any abortion should be allowed (with or without caveats).
This all-out version of PC doesn't seem right to me. Clearly, abortion shouldn't be used as a means of birth control. But what is really at issue here? Is it the fact that the mother in this case is having her fifth abortion? Or is it simply we feel the mother to be morally blameworthy by not using other means of contraception?
My suggestion is that it's the latter interpretation that makes more sense. After all, it's not really the number of abortions that we take into consideration - it's the circumstances of needing the abortion. Consider a woman who's having her fifth abortion because she doesn't like how condoms feel versus a woman who's having her fifth abortion because that's the 5th time she's been r-aped.
It's hard to hold the latter woman morally blameworthy for having the abortion, at least compared to the former case. So it's not really about the number of abortions - or really the act of the abortion at all. As I said, it's about the circumstances that make having an abortion in the first place.
This is why I reject the extreme notion of (PL). Intuitively, it seems like we need another premise to get to the conclusion that all abortions are wrong. This premise would presumably have something to do with an inherent right to life possessed by all humans, or even all living things. It would likely also need to defend premises that could define an unborn fetus as living.
Not only does a moderate version of (PC) seems more palatable, but the extreme version (the only version) of (PL) seems too hard to defend." -Moegreche
Further information to consider.
Abortion arguments side-by-side
A World Without Abortion