I like to emphasize the fact that control of the White House doesn’t matter quite as much for big picture outcomes as people think. But still it does matter a great deal for dozens and dozens of smaller-bore policy issues like this one.It's a very good point. I'll elaborate a bit, after first following up his link by referring you to a good substantive post on the White House's new drug strategy.
Here's my Neustadtian version of what Yglesias said. On the one hand, the presidency is a constitutionally weak office, and so presidents can do very little just because they want to do it. Presidents lose battles all the time; if a president doesn't keep a promise, odds are that it's because he either lost a battle, or made a smart choice not to fight a battle because the costs would be too high. Yes, there are obviously times that presidents just double-cross their supporters, and times when presidents make poor choices about which battles to fight, but my guess is the first of those is actually pretty rare. At the same time, however, a strong president can really affect an enormous number of policies -- virtually anything the government does can be done differently if an effective president makes it a priority.
How many policies? Yglesias talks about "dozens and dozens" but as you can see in the link, something like drug policy itself has over a dozen individual policies to sort through. Remember that the folks at Politifact counted over 500 specific promises Obama made during the campaign. 500. And that's just the specific campaign promises, not the things that come up after the campaign, or the things that Obama didn't want to change but that John McCain might have had he been elected, or the things that Obama intended to do (and may have already done) that weren't expressed as "promises" in a way that Politifact would count them -- for example, I can't find the drug policy items or "enforce labor law" in the their list of promises, although I'll admit I could have missed them. Putting a number on it is impossible, and certainly depends on how one counts things, but we're talking about thousands of potential policies.
Again, what Neustadt taught us is that just swearing in a president doesn't mean that any of those changes are certain to happen. It takes presidential initiative, whether that means personal attention to a policy, or setting up a system that will yield policy persistence. Since there are other players, often with larger stakes in particular issues, it is not at all uncommon for presidents to just lose, even if they are trying to effect change. Not to mention that there are plenty of things that presidents do that don't fit under the category of "policy" -- presidents do a lot of management, or making sure that policy, once decided, is implemented well.
So where does that leave us? It's a real mistake, one that's encouraged by a lot of media coverage and probably by everyone's attempt to simplify complex systems, to think that presidents run the nation. The presidency is -- it really can't be repeated too often -- a constitutionally weak office, and the president really can do almost nothing just because he wants to do it. But at the same time, a determined and effective president can affect hundreds, maybe thousands, of policies, so it really does matter quite a lot who wins the presidency.
One more thing. In most cases, the direction of policy is much more a matter of partisanship than of the individual preferences of a particular man or woman; any conceivable Democrat would have sought to increase enforcement of labor law. But the emphasis on one policy over another, the effectiveness of presidential action, and Hamilton's old favorite, the amount of "energy in the executive" -- each of those may well have a lot to do with the person, not the party or the context. Although one should be careful; a lot of things that at first glance appear to be specific to the person are often, on closer inspection, not so.
An example? Take the Supreme Court nomination, something which we know is of particular interest to our law professor president. We can immediately see that Obama's short list of candidates is radically different than John McCain's would have been: elections matter. I suspect that Obama's short list is virtually identical to what Hillary Clinton's (or Chris Dodd's, or John Kerry's) list would have looked like. It's tempting to think that the decision from that point is where Obama or Clinton or some other Democrat might differ, and that's certainly possible, but it's also the case that interest groups and opinion leaders aligned with the Democrats would be making similar demands in either case, and Senators would be signaling similar things in either case. It's very possible that any Democrat, in other words, would have nominated Sonia Sotomayor, and very possible that any Democrat would come to the same conclusion on the next nominee, but we can't really be sure.