Date math to the rescue. Here's a cute way to convert a Timestamp to an ISODate() of day granularity:
db.foos.find({},{_id:0,TimeStamp:1})
{ "TimeStamp" : Timestamp(1384370105,6) }
{ "TimeStamp" : Timestamp(1391248800,0) }
project1={$project:{_id:0,
y:{$subtract:[{$year:"$TimeStamp"}, 2013]},
d:{$subtract:[{$dayOfYear:"$TimeStamp"},1]},
jan1:{$literal:new ISODate("2013-01-01T00:00:00")}
} };
project2={$project:{tsDate:{$add:[
"$jan1",
{$multiply:["$y", 365*24*60*60*1000]},
{$multiply:["$d", 24*60*60*1000]}
] } } };
> db.foos.aggregate(project1, project2)
{ "tsDate" : ISODate("2013-11-13T00:00:00Z") }
{ "tsDate" : ISODate("2014-02-01T00:00:00Z") }