A constant scan takes either 0 seconds or 2-3 minutes
It appears as though even with a ... WHERE 0 = 1 clause that there will still be a requirement for an intent shared (IS) lock on the table.  Let's prove this:

I will start out by creating a test table:

use TestDb1;
go

create table dbo.MyTestTable1
(
    Id int identity(1, 1) not null,
    SomeInt int not null
);
go

insert into dbo.MyTestTable1 (SomeInt)
values (10), (20), (30), (40), (50);
go


Now that I have my test table, in one session (query window) I'm going to execute the following to put an exclusive (X) lock on dbo.MyTestTable1:

use TestDb1;
go

begin tran;
    select
        Id, SomeInt
    from dbo.MyTestTable1 with (tablockx);
--commit tran;


I can verify the exclusive lock by looking at the sys.dm_tran_locks DMV.  Then in another session (new query window) I do exactly what your query does:

use TestDb1;
go

select
    Id, SomeInt
from dbo.MyTestTable1
where 0 = 1;


At first glance I see that it isn't completing.  Looking at sys.dm_exec_requests, I see exactly why this is the case:

select
    r.session_id,
    r.status,
    r.wait_type,
    r.wait_time,
    r.wait_resource,
    r.blocking_session_id
from sys.dm_exec_requests r
cross apply sys.dm_exec_sql_text(r.sql_handle) st
where st.text like '%where 0 = 1%'
and r.session_id &lt;&gt; @@spid;




I can see here that my ... WHERE 0 = 1 query is waiting on an IS lock for this object (that object_id translates to dbo.MyTestTable1).

I am by no means saying that concurrency is your problem, but by the sounds of it you are exhibiting the symptoms.  The example above is to prove that your aren't exempt from locking and blocking even with a WHERE clause that'll never return data.  

All we can do is guess, so what you need to do when it's "taking a long time" is to see exactly what that request is doing that is taking so long.  If it's waiting on something, then see what it's waiting on.