At the federal level, no major presidential candidate supports EU-style worker protections and mandatory benefits. And not enough congressional candidates support it, not even remotely enough to change anything. In fact, the vast majority are outright hostile to worker rights due to lobbying/capture by corporate interests.
At the state level, there is lots of variance, but even in the states most friendly to workers, it's not remotely possible to reach Europe's level of benefits around vacation, sick leave, maternity leave, let alone the right to organize for these things. There is no political will, and any political candidate who actually has the will could never win a statewide election.
All in all the US has been a success story. Whether there's correlation or causation between that and some of the regulatory and legal environment is hard to say. Maybe it's success is primarily due to resources and geography and maybe the US would be even more successful with a more European style system.
Speaking only for myself, I've found that when I joined a company whose time-off policies I didn't like (only one so far), I just asked for more time off as part of the deal. The response I got was "sure. It's easier for us to give you more paid time off than more money."
Given the current political system(s) in the US, this is practically impossible at the federal level; difficult at the state level; somewhat more possible at the city level (eg New York City's Working Families Party). Third parties exist but generally have almost no influence.
Ummmmmm, Yes?
It's how the people who got ALL the rights we take for grated today did.
Especially our employment rights: https://en.wikipedia.org/wiki/Tolpuddle_Martyrs
Shall we lobby our representatives? This does happen at the state level, and accordingly many states have more pro-worker policies and laws. But change at the federal level is a substantially harder thing to bring.