The Christian Alliance is a new group of Christians who support a liberal/progressive political agenda.
Their position on abortion is to focus on prevention rather than re-criminalization. By "prevention", they appear to mean mostly preventing unwanted pregnancies via contraception, rather than via supporting women when they are pregnant. (They don't mention support for programs that provide non-abortion-related relief for women in crisis pregnancies.)
Progressive/liberals do believe that by supporting policies that provide a more substantive economic safety net, abortions caused by economic factors will decline. On the other hand, conservatives believe that when they support policies that create a vibrant economy, abortions for economic reasons will decline. So, the differences here come down to differences on how one might best create good economic conditions that make pregnant women safe, rather than how one feels about abortion per se.
The Christian Alliance website includes a short comment from a woman who had an abortion:
I was in a bind. At 17, my drinking and drugging had made my complacent about using birth control. One day, naïve and pregnant I vomited in the school parking lot. Neither safe sex nor abortion had been a family option. My denial broke and the tears flowed. I felt like I was in a blind alley, cornered by a street gang composed of my own low self-esteem, cultural shame messages, an abusive sex partner, and my judgmental mother. My friend consoled me and recommended abortion. It was the right choice for me. I know that I made the right decision.It's really unclear to me how a decision that was the result, as she says, of a long list of cruddy circumstances was the right decision. It sounds like having the baby would have been the way to resist and counteract the negative forces in her life, while having the abortion was giving in to them.