The proposed legislation in Texas (SB1) to prohibit abortion at or after 20 weeks post-fertilization is lawful under the United States Constitution. The bill includes robust exceptions for circumstances in which the continued pregnancy threatens serious risks to the life or health of the mother, and even allows for abortion in the case of certain fetal abnormalities. SB1 is, in fact, a modest limitation on abortion that commands a great deal of support across the political spectrum.
The most important point is that there is absolutely nothing in the text, history, or tradition of the US Constitution that precludes the state of Texas from extending the most basic protections of the law to 20-week-old (or older) unborn children who are capable of experiencing pain. This is sufficient constitutional warrant to enact the modest restriction on abortion and its practice that Texas is considering.