The Progressives would mostly be taking away working-class Northern votes from the Dems, and in an era where Northeastern Republicans or those in their ideological mold are always nominated that means New England topples into the GOP column. In the US (leaving aside parliamentary v. presidential) the ballot system is designed to ensure third parties do not receive electoral votes unless one of the parties collapses (1912) or collapse + regional base (1968). The first scenario seems what's likely to occur here given that WWC voters are the core of the Democratic base alongside white urbanites. Nor would Humphrey leave the Dems, he was far too loyal.
I'm not fully clear here. If the GOP is a liberal party, and the Progressives gain working class white support in the North, are both not then left-leaning? Remember, this is before abortion, amnesty, acid, and debates over LGBT issues and capital punishment.
By 1948, the GOP was moving rightward while the Democrats struggled to be a catch-all party. Here, I am proposing that this happens due to the defection of much of the Left to the new Progressive Party, and each therefore having a real base of support in different parts of the country.
Third parties have fared with some success in EVs when they have put forth credible and persistent candidates with actual bases of support outside of the nation's press rooms.