See, I just don't know where you get this from. The democratic party in America is centre-left compared to ANY comparable western government. There are very few democrats in America that propose raising taxes and social spending to the point of left-wing parties in Australia or Europe. Liberalism in Scandinavia would be called socialist or even communist by most American standards. But in the EU its standard fare. The GOP on the other hand is further right than any its contemporaries in the rest of the world. For example, in Britain UKIP is considered far right extremist because they want to slow down and halt immigration...whereas in the GOP thats very run of the mill even for moderates.
If the international stuff is putting you to sleep, let me put it this way: a few years ago Romney proposed a plan similar to Obamacare, 10 years ago Bush supported immigration reform, 30 years ago Reagan supported the Brady Bill, and all the way back in the 60's Nixon formed the EPA. Very few Republicans will take similar stances in this day and age.
The only change in the democratic party is its now more bought-and-paid-for than ever. And lets be honest, they all are.
I'd say both US parties have consistently shifted to the right and the democrats are definitely centre right and are probably further to the right than most European conservative parties and the Australian liberals (conservatives), at least on many issues. The Dems used to be more or less equal to Canadian conservatives although since they merged with the canadian alliance to become the new tories they've gone batshit crazy and are now something like a Canadian Likud cum rogue petro-state.
Also, even the most right wing party in Europe, Australia or canada supports stronger healthcare than anything Obamacare managed to achieve and which by US standards was revolutionary and got him more accusations of "socialism". even the most right wing party in Europe and Australia and Canada supports paid maternity leave of at least 3 months, something the US still doesn't have and is the only industrialized country in the world that doesn't have it. Even Stephen Harper didn't dare touch universal healthcare, paid maternity leave or gay marriage. And no US democrat supports having a social welfare system that would be anything near what Europe, Australia or Canada have, even when these countries have right wing parties in power. and the level of encroachment religion has over US politics would be regarded as backwards and unacceptable by even the most right wing party in europe, except maybe in italy and spain where they have a lot of catholic fascists.
