Here's the motion for a preliminary injunction; here's the heart of the argument (I hope to also post key parts of the state's brief, when that is filed):

Here, in terms of the burdens, the Attorney General's current enforcement threat operates as a ban, whether for all abortions or for all abortions after ten weeks. The Executive Order is in effect for at least thirty days, and in fact could remain in effect for months, which would push many abortion patients past the legal limit for an abortion in Texas. Moreover, even if some patients affected by the order are able to obtain an abortion if the order is lifted sooner than anticipated, they will still suffer increased risks to their health by the delay in access to abortion care. Thus, the Executive Order overwhelmingly harms individuals seeking an abortion.

These harms vastly outweigh any potential benefits from the Executive Order as interpreted by the Attorney General. The State asserts two interests—neither of which is furthered by the Attorney General's interpretation. On its face, the Executive Order is intended to preserve hospital capacity and PPE. Plaintiffs share those interests, but a blanket abortion ban does not serve either one and, in fact, as so interpreted the Executive Order is more likely to aggravate than alleviate the public health crisis arising from the pandemic. As to the first interest, legal abortion is safe, and complications associated with abortion—including those requiring hospital care—are exceedingly rare. Nearly all abortions in Texas are provided in outpatient facilities, such as Plaintiffs' abortion facilities and ambulatory surgical centers, not hospitals. Thus, Plaintiffs' provision of abortion would not deplete hospital capacity.

Regarding the second interest stated in the Executive Order—to preserve PPE—even in the absence of the Attorney General's threat to ban procedural abortion, Plaintiffs have already taken steps to preserve PPE, including by, for example, limiting the number of individuals allowed into the facility and during a procedural abortion and postponing other in-person, non-essential visits that may require PPE. Plaintiffs are exploring additional measures to preserve PPE, such as washable masks and gowns. Moreover, Plaintiffs either do not use N95 masks or do so only rarely, and this is the PPE that appears to be in shortest supply in battling the COVID-19 pandemic in Texas and around the country. As such, banning abortions does little to nothing to prevent the "deplet[ion]" of the personal protective equipment needed "to cope with the COVID-19 disaster."

Even before the Executive Order, Plaintiffs had taken steps to preserve PPE by minimizing the number of encounters a patient needs for care, but Texas law restricts this flexibility. Plaintiffs could make further progress in preserving PPE, as well as reducing overall contagion risks during the pandemic, were Defendants willing to consider temporarily waiving medically unnecessary abortion restrictions that limit their ability to adapt to this crisis—such as Texas's requirement that patients make an extra trip to the health center and receive an ultrasound before returning for an abortion.

Indeed, far from being necessary to address the COVID-19 crisis, an interpretation of the Executive Order that broadly prohibits abortion could well exacerbate the COVID-19 crisis, including by forcing patients to attempt to travel to other states to try to access abortion care, and potentially using public transportation, even though public health experts have advised the public to minimize activities outside the home. Moreover, the Executive Order may delay access for patients experiencing health problems because providers are uncertain as to whether these problems meet the Executive Order's emergency exception, which could endanger those patients and potentially require that they receive more invasive care (with attendant use of PPE) or even hospital-based care. Finally, delaying patients in accessing abortion ultimately requires increased use of PPE. Even if the Executive Order is ultimately limited to thirty days, this delay will push patients early in pregnancy now beyond the time for which they would be legally eligible for medication abortion (PPE is not needed to hand a patient pills), instead requiring one-day aspiration procedures. For some patients, the delay will push them into two-day D&E procedures, which necessarily require more PPE than a single visit or a medication abortion.

Even if banning or restricting abortion during the COVID-19 crisis would result in some small, temporary preservation of PPE, the harm to patients from not being able to access abortion for a month or more, if ever, is extreme and simply cannot be outweighed by any benefits of Defendants' application of the Executive Order. While Plaintiffs are mindful of the need for everyone in Texas and around the country to do their utmost to mitigate the effects of COVID-19 on our health systems, the reality is that very little, if any, PPE would actually be conserved by banning or restricting abortion. Most procedural abortions in Texas are single-day procedures, where a patient encounters either one or two clinicians, who each wear, at most, a paper mask (not an N95 respirator), two-to-three pairs of gloves, and a gown. However, patients forced by Defendants to wait until the middle of the second trimester or later might be forced to undergo a two-day procedure, which would mean two consecutive trips to a health center; twice as much contact with health care providers; and at least twice the amount of PPE used—for a total of three visits.