OP, my only objection to your comment was the misnaming of the fallacy as a straw-man.  The assertion that someone (even an unnamed someone) actually holds the weakened position is a critical requirement for a straw-man argument.  It is not enough that an argument be weak to be a straw-man; behind every straw-man, there must first be a “man”.  You give an excellent example of why Obama’s quote does not qualify.

Had Obama stated:

So, one option is to pick dandelions. We say, well, it’s too expensive for us to make some short-term investments in health care. We can’t afford it. We’ve got this big deficit. Let’s just pick dandelions and hope that fixes the health care system.

it would be clear that this is a red herring and not a straw-man fallacy.

Drudge cuts off Obama’s quote shortly thereafter but the full statement is:

So, one option is just to do nothing. We say, well, it’s too expensive for us to make some short-term investments in health care. We can’t afford it. We’ve got this big deficit. Let’s just keep the health care system that we’ve got now.
Along that trajectory, we will see health care cost as an overall share of our federal spending grow and grow and grow and grow until essentially it consumes everything. That’s the wrong option.
I think the right option is to say, where are the game changers, the investments that we can make now that are going to reduce costs, even if they don’t reduce them this year or next year, but 10 years from now or 20 years from now, we are going to see substantially lower costs.

The right / wrong distinction makes this sound like a dilemma but is it a false dilemma?  Is there an option that lies somewhere in between “doing nothing” and “finding game changers … that are going to reduce costs”?  Maybe.  In my opinion, his language is sufficiently imprecise to pin this fallacy on him.  Indeed, introducing market reforms may be one such game changer even though it’s not one that he personally supports!  He then goes on to say why he feels his particular game changers will work (including a mis-characterization of the position held by big-Pharma, IMO).

Transcript quoted from: http://www.c-span.org/pdf/obamainterview.pdf

Hector, Obama certainly doesn’t ascribe the straw man argument in regards to health care to any particular person or party, but he nonetheless uses one when he says:

So, one option is just to do nothing.

That is certainly an easy pile of straw to knock down.  Yes, one option is to do nothing.  Another option is to depend on Scientology to solve our health care problems.  Yet another is to pick dandelions.  No serious person with an influence over the health care debate sees any of these options as a solution.  

An intellectually rigorous person (as he is supposed to be) would not need to use this straw man technique over and over again.  A thoughtful policy wonk (as he is also supposed to be) would at least mention the actual position of the other side on something like the issue of controlling health costs (which in this case would be some kind of market-based reform) before debunking it with his own reasoning.

by Hector N. Fertig

A technical point just to get my feet wet on this site…

I don’t think I would categorize Obama’s health care argument (limited to the Drudge article) as a straw-man fallacy as he never says that anyone else holds this position and only hypothetically ascribes it to “we” – though it is close. It sounds more like either a false dilemma or a red herring to me. He begins…

“Well, we are out of money now… If we don’t reduce long-term health care inflation substantially, we can’t get control of the deficit.”

Possible paraphrases of the stanza you quoted:

1. “There are only two possible options, my way or do nothing and here are the consequences of doing nothing.” – false dilemma (assuming there is a third option such as the one you already indicated)

2. “Let me give you an example of an extraordinarily bad approach to this problem…” – red herring (why bring up something like this that no one has suggested?)

By contrast, the stimulus package statement really does sound like a classic straw-man argument to me.

The New York Times agrees.

Obama, once again, attempts to advance a policy proposal by setting up a straw man, this time on health care:

So, one option is just to do nothing. We say, well, it’s too expensive for us to make some short-term investments in health care. We can’t afford it. We’ve got this big deficit. Let’s just keep the health care system that we’ve got now.

This is the same tack he took with his stimulus package (“some say we should just do nothing…”) and his budget.  But who in the political arena wants to do nothing when it comes to these problems?  Name some names!

Of course, he can’t say “some want to control costs by introducing market reforms” because that would force him to actually have a substantive response.  And as we heard in his speech on Gitmo the other day, substance is not his thing (still waiting on your plan for Gitmo, Mr. Prez, love, Harry Reid).