Using abs() prevents using a datetimefield index. I propose to have one select for the closest before and one select for the closest after, both using the index, and picking the closest of them afterwards:
create table `table` (datetimefield datetime key, one varchar(99));
insert into `table` values
('2014-06-01', 'a'), ('2014-12-01', 'b'),
('2015-01-01', 'c'), ('2015-02-01', 'd');
set @d = '2014-12-10 09:45:00';
select * from
(
( select *, TIMESTAMPDIFF(SECOND, @d, datetimefield) as diff
from `table` where datetimefield >= @d
order by datetimefield asc limit 1
)
union
( select *, TIMESTAMPDIFF(SECOND, datetimefield, @d) as diff
from `table` where datetimefield < @d
order by datetimefield desc limit 1
)
) x
order by diff
limit 1;
http://sqlfiddle.com/#!2/bddb4/1