Bear with me, this is really worth understanding to get what is going on now. In 1993, Yeltsin got into a fight with Russia's first democratically elected Parliament. The fight was about many things, but most of all, it was about a new Russian constitution that Yeltsin was trying to force through, which concentrated power in the hands of the Russian President, at Parliament's expense, allowing the President effectively to rule the country with a minimum of interference from Parliament. At the time, it was widely regarded as a necessary temporary measure, to help get Russia out of an economic hole. Not surprisingly, Parliament didn't appreciate being bypassed and refused to approve the new Constitution, but eventually the President adopted it anyway, by signing it into effect himself. Which was of course illegal - one individual cannot adopt a new Constitution, but this is what happened anyway.
In the resulting battle which amongst other things involved tanks shelling Parliament, the Western media overwhelmingly supported Yeltsin, because he was seen as the reformist, and parliament had been rather slow at allowing economic reforms to be pushed through. The Parliamentary deputies were made out in the western press to be hardline communists, reactionaries - which some undoubtedly were, but some of the key leaders of the parliament, in particular Rutskoi had supported Yeltsin a couple of years earlier against the attempted 1991 putsch and became Yeltsin's Vice President. And don't forget that this was Russia's first democratically elected Parliament since the Revolution.
In short, Yeltsin won the battle, Parliament was left a largely burnt out shell (the building it was in, the White House, became popularly referred to as the Black House because of the charring on the facade), and the constitution giving overwhelming power to the President was recognised. Six years later, Yeltsin retired as President and Putin took over.
Article 107 of this new Russian constitution gave the President the right to reject any law adopted by the Russian parliament. Once rejected the law could only be passed if parliament re-adopted the law this time by a two thirds majority. In most situations, unless parliament has a very serious disagreement with the President and is not constituted of deputies largely from the President's party, a two thirds majority is a very high barrier. For most practical purposes, this gave the President a right of veto over Parliament's laws, and means that Parliament would only challenge the President in the most extreme circumstances. Normally, there would be little point in Parliament fighting to push through laws that it knew the President would veto.
That aside, because the Government (which because of the constitution, effectively meant the President, because he also had given himself the right to appoint the Government) had control of most of Russia's media outlets, the President had the possibility to maintain his popularity through the careful control of news. Putin adopted a systematic policy of suppressing or taming the relatively few mainstream independent outlets.
That was Russia - what relevance does this have to what's going on in Ukraine?
The loss of democracy in Russia twenty years ago (with vital help from western governments, who must be kicking themselves now), provided a nice model for Putin/Medvedev to bring Ukraine back under the wing of Russia. A President who has power concentrated in his hands, could be brought more and more under the heel of Moscow, using financial incentives - $15 billion in aid, plus the stranglehold Russia has over gas supplies to Ukraine, a carrot-and-stick approach. If there was an unpredictable and stroppy Ukrainian parliament in the way, no central control by an individual who could be brought to depend on Moscow, and no effective manipulation of public opinion, Russia would be wasting its money. If it could be done in neighbouring Belarus, with a complete stranglehold by President Lukashenko (who really depends politically on Moscow), then why not Ukraine?
The Russian and the Ukrainian constitutions have an awful lot in common. The writers of the Ukrainian constitution read the Russian one closely. Article 94 of the Ukrainian constitution contained a provision very similar to Art 107 in the Russian constitution - giving a Presidential right of veto over Parliament's laws. On the face of it, the Ukrainian parliament ought to be as emasculated as the one in Russia. But in Ukraine, because the media is not as closely state controlled as in Russia, and because after 2004 the Government wasn't (for a while) appointed by the President, there was still a possibility of striking some kind of balance short of complete power - popular opinion can still be vitally important and is not easy to control in Ukraine.
In 2004, after the Orange Revolution in Ukraine, popular demonstrations managed to get some limitations imposed on the Ukrainian Presidential powers. These limitations didn't reduce the impact of the critical Article 94, but they did at least take away the President's power to appoint the Prime Minister and to dismiss the Cabinet. And without the direct ability to control the Government, an essential leg of President's absolute control is taken away. Since 2004 President Yanukhovich has managed to get these limitations on Presidential power overturned using rather dubious methods. Reversing this accretion of Presidential power has been one of the key demands of protestors (and earlier today, the President agreed to reinstate the 2004 constitution, removing his ability to control the Government so directly).
So Putin/Medvedev think they need Ukraine to have a strong President and a weak Parliament, just like in Russia, or Belarus. It is their only hope of getting Ukraine back under their wing. In any case, this is the Russian model, comfortably familiar - the hackneyed old chestnut that 'Russia needs a strong Tsar'. That was why Medvedev's response to the bloodshed on Maidan was that "the active authorities in Ukraine need to be legitimate and effective, not a doormat for everyone to clean their feet". Which was not only a rather likely to alienate a lot of Ukrainians, but also contains an implied insult to Yanukhovich, which seems, apart from anything else, politically inept. By 'active authorities' of course, Medvedev meant the President. Presidential power meant Russian power - Putin's power. Without an all-powerful - and necessarily ruthless - Ukrainian President, there could be no Russian aid to Ukraine.
Fortunately for Ukraine, while much of the media is state-controlled, the Ukrainian government has little prospect of gaining such an effective stranglehold over mass information as was possible in Russia. Ukrainians are too close to Europe, especially to Poland and Germany, for this to happen. Information and travel is much more porous across Ukraine's borders than for Russia. Journalists have had a longer time to get used to thinking for themselves. The Putin model can only work in a situation where it is possible to manipulate public opinion, and where the Presidential power is reinforced by the economic power given by gas and oil production (which Ukraine lacks - it has instead dependency on Russia). And there is the issue of Ukrainian nationalism, which makes domination from Moscow far more difficult.
Personally, I doubt whether Putin/Medvedev have fully appreciated why their own model could not work in Ukraine. If they are beginning to understand it, it is ten years too late. Yanukovich at least is close enough to know this, which is why he hasn't dared (so far) to act decisively - doing so could only end in disaster, civil war. Which could quite likely spread to Russia. Putin's policy of dominating Ukraine is I think ultimately doomed to failure and counter-productive for Russia, but the question is what the cost of Russia's ineptitude will be.
That's my perspective on what has been happening anyway.