That's why Australia is being brought up: the way they use "liberal" as a conservative political demographic has as much to do with how the US uses it as European countries do. Which is to say zilch.
People said that the Democratic Party was centrist during Obama's years, during which period many Democratic senators were closer to Joe Manchin than Bernie Sanders in terms of policy alignment.
Today, the Democratic Party today is economically left-wing: they're in favor of funding welfare, pro-union laws, protectionist economic policies (such as tariffs), rent control (not universally), and workplace safety regulations. They're socially left-wing: they're in favor of criminal justice reform (including abolition of the death penalty), racial equity, LGBT rights, a pathway to citizenship for undocumented immigrants, and access to abortion.
There's not a thing about them that's center-right.
It's never been particularly accurate. Anything as large as the modern democrat party is going to have all sorts of opinions, which is one thing a lot of, uh, twitter style opinions, tend to miss. Ocassio-cortez and Manchin were both technically part of the democrat party at the same time, for example.
Among whom? In what country would their policies be center right?
Left/Right is a pretty rough categorization to begin with, and things we associate with it in a liberal democracy might not hold globally. In China, the left wing of the CCP and other parties is generally regressive, wanting to go back to policies more in line with Mao, while the right-wing is economically more akin to our european liberals, but also socially progressive for things like lbtq rights. In South America, the left wing is usually economically statist and redistributive, but might be rather conservative on some social issues. There's also the whole liberation christianity movement. Japan as a country is way more conservative than the US.
Going back to a US-EU comparison: I think it is fair to describe the Democrats as centre-right on economic policy, especially when it comes to taxation. Outside of the UK, almost all countries in the EU have less qualms about high taxation levels, and it is obvious that a lot of senior democrats are in the pockets of rich donors and Wall Street.
On social issues I feel like it is different though: Open borders and immigration in general is significantly more controversial on the left side here in Europe. Things like being against against voter id is considered cooky by basically everyone. And the US is often leading the way on issues, as can be seen with gay marriage and cannabis legalization.
A simplistic left/right analysis does not do justice to the complexities of voter ideology and policy. In fact, I think the more this kind of analysis makes sense, the less mature the democracy tends to be, as it indicates that people look at it as a teamsport.
My point is that the Democrats are very left wing on some issues when compared to the world. Sure not all democrats are as hard into those things, but they are still very into it compared to what is normal in other countries.
So cooperating with Republicans might not be problematic in an economic kind of sense, but given that Democrats are so strongly to the left on other issues its a no-go. That was the topic.