Actually no. In most of Europe one refers to these parties as what the German's call Volksparteien (People's Parties). The Democrats, as the Replications, unfortunately, have become over the past few decades quite polar. As a former Cloakroom Keeper commented to me "it used to be that Speaker and House Minority Leader would argue on the floor but play golf together, today they really do hate each other".
The once American left has been hijacked by an oddball mix of nut-cases funded by North Korea, Iran and whoever has an agenda to subvert America. The left marches hand in hand today with terrorists and arab nationalists. Its hard to see who is more dangerous the hijacked left or the new right (which too has been hijacked by neo-fascist libertarians).
Right and left have gotten incredibly confused in Europe (as well). Parties like the Vlaams Blok which used to wear SS uniforms and deny the Shoah now are called the Vlaams Belange (the Blok was forbidden as anti-constitutional) and have morphed into a pro-Israel, pro-liberty party completely hijacking anti-globalization and cultural integration issues. While Vlaams Belange speaks out against gencoide the European "left" marches alongside the Belgian AEL (Arab European League) who have called for violence against Jews. Parties like the DKP (German Communist Party) have even gone as far as to lend support to suicide bombing and jihad--- nothing like hearing the cries of "Khybar, Khybar", "Allah.." (Khybar it should be noted was an Oasis near Medina that was inhabited by Jews until violently conquered by Mohammed in 620 CE and then completely ethnically cleansed--- Jews and Christians alike-- by Caliph Ulmer in the following years.) to the occasional kill the jews (in arabic) at a "peace rally" with DKP flags flying alongside Hamas, Hizbolah and Milli Gorus (Turkish nationalist Islamic movement) green banners. Go over the UK and there you'll find the same with the left in bed with MAB (the Muslim Brotherhood British franchise) on the one side with English Defense League.. The left marching with Muslim fascists and the once Europe neo-fascists re-labled as the defender of occidental culture and even freedom (for example Pim Fortuyn). The story repeats itself throughout Europe..
Perhaps the concepts of left and right have become something else.