Most people who are pro-choice are "pro-choice, with caveats." For example, most pro-choice people I'm aware of are quite fine with abortions being illegal in the final trimester, except for the health of the mother. In most countries, pro-choice parties and candidates are actually more stringent, usually allowing elective abortions only before the 20th week.
I'm a bit curious, then, as to why the pro-life movement seems so very absolutist. The very admittance of the pro-choice movement to restrict abortion in any capacity shows that, for all the political rhetoric, there is an understanding that the stage of fetal development has to factor in to a woman's right to an abortion. You might say that this is because pro-lifers view every abortion as murder, and are thus unwilling to accept any half-measures, but I'm not sure that's necessarily the case. There's an odd level of the deontological, if/then logic present among pro-life groups that you just don't see among the pro-choice.
To reiterate: the vast majority of the pro-choice movement, despite having similar deontological rhetoric, doesn't support completely unrestricted abortion regardless of the stage of fetal development. Pro-lifers, however, can't consider themselves pro-life unless they support the total illegality of all abortion, for any reason, even in some cases rape or incest.
This is (a small) part of why I don't think the traditional pro-life view is very tenable. Its commitment to this kind of logic has very little persuasive power in the real world, and any inroads against abortion access that have been made by the pro-life has been invariably met with massive resistance (understandably so). Consider instead a pro-life ethic that, at the very least, was willing to echo the pro-choice movement's embrace of the practical, a tacit acknowledgement that there really are multiple factors at play even if we presuppose the total personhood of the human from conception. Preventing unwanted pregnancies to begin with, supporting improved adoption laws, increasing social safety nets, making birth control cheap and easy, while not abandoning the moral arguments against elective abortions (which I still find to be compelling), would find a natural home alongside aspects of the pro-choice movement that hope for abortions to be "safe, legal, and rare."
tl;dr, I really hope that Justin Amash clarifies his stance on things like abortion and immigration, even if he really doesn't have much power to do anything about the former.