The only way I ever found to do this was to pass in the ms since epoch:
e.g.
shard01:PRIMARY> db.foodle.find()
{ "_id" : ObjectId("5143a2503924ff36ff355335"), "id" : 1, "ts" : ISODate("2013-03-15T22:36:00.853Z") }
{ "_id" : ObjectId("5143a2553924ff36ff355336"), "id" : 2, "ts" : ISODate("2013-03-15T22:36:05.775Z") }
{ "_id" : ObjectId("5143a25b3924ff36ff355337"), "id" : 3, "ts" : ISODate("2013-03-15T22:36:11.789Z") }
$ mongoexport -version
mongoexport version 2.2.0
$ mongoexport -h localhost -d test -c foodle -q '{ts:{"$gte":new Date('`date -d "2013-03-15 22:36:05" "+%s000"`')}}'
connected to: localhost
{ "_id" : { "$oid" : "5143a2553924ff36ff355336" }, "id" : 2, "ts" : { "$date" : 1363386965775 } }
{ "_id" : { "$oid" : "5143a25b3924ff36ff355337" }, "id" : 3, "ts" : { "$date" : 1363386971789 } }
exported 2 records
Would love to hear of an easier way if someone knows of one.