It's not hard to unwind a myth when you start by creating a straw man. Undoubtedly, in a world occupied by birthers and truthers and various other stripes of gullible or forgetful people, some are misinformed about the duration of the Democratic supermajority. Nevertheless, for a time, one existed. And there really was a Democratic House majority throughout [the first two years of] Obama's first term. (The way Thucydides phrased it, we can be forgiven for reading it to mean the Senate supermajority existed for two years.) And the Democrats really did miss the opportunity to pass one of their perennial wish items - the easiest would have been to raise tax rates.
Back to Canada - it's a majority government, and it campaigned on something bearing more than a little resemblance to Hopenchange ("Real change" being the campaign slogan which replaced the earlier "Hope and hard work"). The Senate can - if it wishes - throw in a wrench. But the only thing standing between the Liberals and whatever they want to pass in the House is themselves. The NDP do need to keep their powder dry; if the Liberals stumble, voters may not yet be ready to re-install Conservatives and may not even be ready to re-install Libs or Cons as a minority, which would give the NDP another shot.