The left is not a hivemind. There are people who self-identify as liberals but not progressives, and there are people who self-identify as progressives but not liberals, and there's those who mix and match.
For example, being liberal usually implies greater freedoms, such as being pro-choice. However, it can also be pro-gun ownership, or anti-war, pro-research, etc. To me that's the dichotomy the U.S. is facing is really about the progressives and religeous conservatives duking it out, but (I'd argue) most people are much more moderate.
It's interesting to me that a third party (libertarians, or someone else) can't capture that group. As many liberals differ pretty substantially from the progressives, and concervative minded people just lump liberals and them together because they all identify as Democrats
In fact, I prefer to classify political views differently, by splitting them into two buckets: those who have figured out that every issue needs an actually effective solution, and those who follow their ideologies blindly.
Fortunately in the UK there's another voice at the table in between the extremes. People tend not to vote for them because of fear, and a misunderstanding of the soft power available in politics.
The fundamental problem with the Libertarian ideology is that the emergent outcome is of a fully economically captured state.
If I started a political party and wanted to capture myself. I'd just steal all the good ideas from all the parties.
Personally, I would prioritize extensive political reform and reconstruction, but I fear the level of financial capture and constitution worship in the United States makes thus impossible.
For the most part, my politics are similar to progressives - higher taxes, public healthcare, more expansive welfare (I support UBI), and social justice in general.
The reason why I don't consider myself a progressive is that I feel that the progressive ideology in US has largely abandoned the traditional concept of natural individual rights in pursuit of all these goals. You have people openly claiming that freedom of speech is not worth it if it gets in the way of criminalizing offensive speech, for example. Or how due process is an outdated notion that makes it hard to prosecute sexual harassment properly. Basically, the further left you go with progressives, the more individual rights are sacrificed to collective ones.
That, to me, is the line past which you can no longer meaningfully call yourself a liberal, since liberalism is all about individual rights, ultimately. Where left-wing and right-wing liberals differ is on the matter on how to best maximize those rights, and to what extent government regulation is advantageous or detrimental to that, especially on economic matters.
And, to some extent, on what those rights are, precisely - for example, I don't consider property rights to be fundamental natural rights (but then again, neither did Thomas Jefferson, and he sure wasn't left-wing!). Note, it doesn't mean that property is a bad idea - I think it's a social construct that is broadly useful, it's just not an absolute right (and hence taxation and wealth redistribution is not inherently an infringement on such).