The NYT article actually goes into detail of the step by step process in the negotiation and why it failed, your Time article shows absolutely no signs of actually interviewing anyone involved in the investigation, just left wing opinion swill. Maliki wanted troops, a lot of them.
The Politifact article has Martha Raddatz claiming that the White House wanted 10,000 troops, but then goes on to confirm that the Iraqis and US Military advisors wanted 16,000 troops and then goes on to confirm the NYT story that Obama only offered 1500 troops.
That they then go on to say that Raddatz misleading and wrong statement is "mostly true" is simply another piece of evidence that Politifact is a dishonest joke. "She's wrong, Obama actually only offered 1500 troops... but he had earlier lied about wanting 10,000 troops that he never offered so we rate this lie mostly true."