Yes, they are neoliberals, which are hardly left by international standards. European social-democratic parties, which are the traditional Euro center-left, are generally on the back foot right now.
Oh, I just looked the naming up. Apparently the US is still in the 18xx calling left wing liberals?
TBH this whole left-right thing is pretty new in the US. The political science term is "ideological alignment" (we didn't really have it for a long time due to our weird party system) if you want to read about it. This is changing now to an extent, but there was also a taboo for a long time against identifying as being a leftist, what with McCarthyism, COINTELPRO, etc.