how to efficiently update tuple in many-to-many relationship?

I have 2 tables (A,B) joined in a many-to-many relationship via a
join table ("membership"), where updating table A based on table B
takes a very long time.

Tables A and B have oid primary keys (a_id and b_id respectively).
The join table, "membership", has its own oid primary key
(membership_id), as well as foreign keys "a_id" and "b_id".

A SELECT query across all 3 tables takes 12 seconds.
"SELECT count(*) FROM a JOIN membership USING(a_id) JOIN b USING
(b_id) WHERE b.is_public = true"

But a simple UPDATE using the same SELECT query takes 30 minutes to
an hour.
"UPDATE A set is_public=true WHERE a_id IN (SELECT count(*) FROM a
JOIN membership USING(a_id) JOIN b USING(b_id) WHERE b.is_public =
true)".

What am I doing wrong here? I'm not sure how to diagnose this further.

Here's the output from explain:
db=# EXPLAIN SELECT a_id FROM a JOIN membership USING(a_id) JOIN b
USING(b_id) WHERE b.is_public = true;
------------------------------------------------------------------------
-----------------------------------------
Hash Join (cost=167154.78..173749.48 rows=51345 width=4)
Hash Cond: (a.a_id = membership.a_id)
-> Function Scan on a (cost=0.00..12.50 rows=1000 width=4)
-> Hash (cost=144406.48..144406.48 rows=1819864 width=4)
-> Hash Join (cost=417.91..144406.48 rows=1819864 width=4)
Hash Cond: (membership.b_id = b.b_id)
-> Seq Scan on membership (cost=0.00..83623.83
rows=4818983 width=8)
-> Hash (cost=348.52..348.52 rows=5551 width=4)
-> Index Scan using b_is_public on b
(cost=0.00..348.52 rows=5551 width=4)
Index Cond: (is_public = true)
Filter: is_public
(11 rows)

db=# EXPLAIN UPDATE a SET is_public = true WHERE a_id IN
( SELECT a_id FROM a JOIN membership USING(a_id) JOIN b USING
(b_id) WHERE b.is_public = true);
------------------------------------------------------------------------
-----------------------------------------
hash in join (cost=281680.17..370835.63 rows=1819864 width=90)
hash cond: (public.a.a_id = public.a.a_id)
-> seq scan on a (cost=0.00..47362.09 rows=2097309 width=90)
-> hash (cost=258931.87..258931.87 rows=1819864 width=8)
-> hash join (cost=73996.36..258931.87 rows=1819864 width=8)
hash cond: (membership.a_id = public.a.a_id)
-> hash join (cost=417.91..144406.48 rows=1819864
width=4)
hash cond: (membership.b_id = b.b_id)
-> seq scan on membership
(cost=0.00..83623.83 rows=4818983 width=8)
-> hash (cost=348.52..348.52 rows=5551 width=4)
-> index scan using
loc_submission_is_public on b (cost=0.00..348.52 rows=5551 width=4)
index cond: (is_public = true)
filter: is_public
-> hash (cost=47362.09..47362.09 rows=2097309 width=4)
-> seq scan on a (cost=0.00..47362.09
rows=2097309 width=4)

Thanks,

Drew