"I have doubts the US will change its approach to the situation and wonder therefore why troops still remain there. I also wonder, among americans who opposed the war before it started, how many want actually the troops to stay there for at least one more year (thinking they can still make a difference after all) as oppsoed to those who understand it's no use."

I'm sure that US will change it's approach- as conditions change they adapt.
And also since Iraq is a sovereign nation and it's leadership were democratically elected, Iraq will change it's approach as conditions change.
As far as Coalition Forces in Iraq and how long they will stay and/or take on different roles, a significant factor will be the Iraqi government and it's choices. For instance, if the Iraq govt wanted Coalition Forces to leave a immediately, one could expect some some back and forth discussion in this regard, but ultimately the Iraq govt could insist that all Coalition force leave within say 6 months- and would get this outcome.

But if the Iraq for some strange reason wanted more Coalition Forces in Iraq- this would something less likely that they would get, though they could capable of damaging the current American administer by doing this in a public way- it's a stick they could threaten to use if they had any need of this kind of stick. An example where this might realistic, is that if some Iraq leaders wanted a particular area brought under forceful control, in which Coalition forces were attempting another approach or other areas had higher priority. More specifically, say Iraqi political leadership favored the idea of "expanding the green zone" in regards to Baghdad- and they wanted American and UK forces providing most of security force that this would require. Or say pool Iraq security forces in Baghdad- and Coalition Forces would used to strenghen those areas that Iraqi forces were drawn from.
Now, whether this was a good idea or not isn't my point, but rather that if Iraq leader wanted this approach to be taken, they have the political power to bring this about.

It seems to me that most critical aspect is improving the quanity of Iraq miltary forces so as to reduce their losses. This a hard metric to gage because the better trained the more these force can be directly engaged and I don't have exact numbers. But from http://www.state.gov/documents/organization/67561.pdf
Iraq has as of May 31 2006: 145,500 police and 117,900 miltary with total security force of 265,600
At: http://icasualties.org/oif/IraqiDeaths.aspx
For Iraqi Police and Military Deaths:
Mar-06 193
Apr-06 201
And total since Jan 2005 being 3444
And for comparison Coalition forces in that time frame was:
Mar-06 82
Apr-06 33
And total since Jan 2005 being 1215