(err.. re Val's ramblings...)
No, it comes down to what the aims of that government are. "Big" or "Small" is entirely irrelevant to that, no matter how loudly you bleat it out.
If you're talking about left v right in a modern society, you need to break it down into social and economic aspects. Socially, the left is progressive and ultimately quite liberal(/libertarian!) in advocating as much personal freedom as possible while not impacting others (hence drug laws, abortion, etc), while the right is driven more by conservative/religious values. There are obviously blurrings in there where issues overlap and cross over for various factors, but broadly speaking that's the gist of it.
Economically, leftists seek an 'equality', aiming to support the disadvantaged at the expense of the elite, while the right does basically the opposite, redistributing towards the top.
No, it's not about more or less government. That's a side-effect.
Right-wing politics supports the wealthy & powerful. Many of those wealthy and powerful are hampered in their pursuit of further wealth and power by pesky government regulations designed to stop them raping the rest of the populace, so they are naturally opposed to that. On the left, it is that government influence which protects the vulnerable from those that would exploit them.
However - the right can also benefit from 'big government'.. The likes of Lockheed, Boeing, GD.. they make vast amounts of money thanks to what can only be described as right-wing politics, and they are absolutely reliant on big government... kinda like Porsche, Krupp, Henschel and others were in Nazi Germany, and there you have your tie-in to left v right. The rise of the elite in the communist USSR was not a systemic aim of the politics, but a corruption of it. Conversely, Nazi Germany was openly and proudly focused on further elevating and rewarding the elite in the belief that that would flow on to the rest of the people.