This is a fairly complicated subject, that really doesn't come down to liberal vs. conservative, or democrat vs. republican, imo. In a perfect world, which we do not inhabit, everyone who is willing to do an honest day's worth of work, would be paid a living wage.
However, jobs that pay minimum wage are not necessarily intended for people trying to earn a living. They are often students or others who work at part time jobs that don't necessarily require a lot of skill. Raising the minimum wage has been shown to cause employers (particularly, non-small business employers such as national food chains, or national stores) to replace those minimum wage workers through automation.
So, like a lot of well intended yet naïve liberal policies, raising the minimum wage could likely have unintended, yet negative result in the form of job elimination. Sure, if you're a minimum wage worker who is one of the lucky ones who doesn't lose their job, you'll be making more. But what about those unfortunate individuals who are laid off?
Like I said, not a simple issue, and not easily dropped into the traditional identity boxes when it comes to how people view the issue.
The first link below is to a Congressional Budget Office analysis of raising the federal minimum wage to various thresholds ($10/hr, $12/hr, or $15/hr), and the second is to a Forbes article discussing the issue. The attached image is from the first link.
https://www.cbo.gov/system/files/2019-07/CBO-55410-MinimumWage2019.pdf
https://www.forbes.com/sites/jackkelly/2019/07/10/the-unintended-consequences-of-the-15-minimum-wage/?sh=d78d3bfe4a7c