It's low-priority because guns are much scarier on the news than their actual death counts warrant. More people die in car accidents every year than have died in the entire history of the United States in mass shootings--yet mass shootings are disproportionately used as a talking point. Yearly motor deaths are an order of magnitude more frequent than gun deaths, and that's if you count the more than half of gun deaths which are suicides--if you want to protect yourself from guns, simply not owning a gun is an effective measure. If liberals took proportional action with regard to harm on car safety to how we act on gun safety, we'd be pushing for frequent re-testing for licenses, lower speed limits, easier loss-of-licenses for repeat bad drivers, stricter drunk driving laws, etc. But that's not what's happening.
It loses us a lot of battles, because it alienates a lot of potential allies. True libertarians, for example, tend to be fairly pro-choice, but don't feel strongly about it, but very pro-gun, and feel very strongly about it. We'd have them on our side in votes relevant to abortion a lot more often if we didn't alienate them with regards to gun rights.
https://en.wikipedia.org/wiki/Gun_violence_in_the_United_Sta... https://en.wikipedia.org/wiki/Motor_vehicle_fatality_rate_in...
Mass shooting != gun violence. Roughly the same order of magnitude of people die from motor vehicles & firearms in the U.S., but very few people die from mass shootings.
I think I would agree liberals may overly focus on mass shootings because handguns are killing most of the people but gun violence is a real problem.
For example, whenever the pro-choice side hears someone from the other side propose regulations about requiring permits for clinics that perform abortions (something that in principle they might agree to), they fear that the person proposing the regulations isn't really pro-choice but only says that because outright banning abortion would not be politically feasible, thus they fear (rightfully so, since it has happened) those regulations will be so onerous or badly implemented that it will result in a de-facto ban on abortion, maybe those permits will be very hard to get or maybe the organization handing them out will be understaffed and underfunded (or both). Similarly, whenever someone who is pro-guns hears someone talking about mental health checks before owning guns (also something they might agree with in principle), for example, what they fear is that this system will be abused to deprive as many individuals as possible of their rights without due process.
Thus, in this situation, neither debate will move forward because pro side does not believe that the anti side is proposing any legislation in good faith, and the reason they believe so is that in many cases that has blatantly been the case, leading to farther spreading of the divide.
Additionally, as you say, someone might be both pro-choice and pro-guns but the political situation is such that they have to choose one or the other, and thus they choose the one they hold dearer to them, usually one that affects them more personally. Unfortunately for the pro-choice crowd, gun control laws seem to personally affect more people in the US than abortion laws.
To be fair, when speaking freely, the pro-life side admits that this is their goal. That is, most pro-life advocates proudly admit that outlawing abortion is their goal. The pro-choice side is so wary of these additional regulations because (as they are currently proposed) (a) their only possible outcome is to close lots of clinics, and (b) the argument that these regulations improve patient care is laughable.
Contrast that with the gun-control debate, where the mainstream gun-control "side" is not advocating for a ban of all guns. Yes, they are in favor of banning some forms of guns (i.e. guns which were banned in the late 90s in the US) and things like mental health and better background checks, but a complete banning of guns is not something that they are arguing for.
In the abortion debate, the "reasonable regulations" are always proposed by abolitionists. The goal is never to make abortion safe and available, it's always to make it burdensome and difficult for both the provider and the patient. Newly empowered by the Trump administration and the sense that they have a new supreme court that will agree with them, they're dropping this tactic and have resumed pushing for abolition.