Android get items from sqlite db with date of today or previous

I'm struggling with the implementation of dates in SQLite3 (for android). According to the documentation (http://ift.tt/148oIVm and http://ift.tt/1mOgs1D), SQLite doesn't have datatypes for date and time specifically and therefore it can be either stored as a TEXT or as an INTEGER. I've tried both, but they give the same erroneous results. After reading a lot on the internet and trying everything I can think of, I come here as a last resort.

So, now for the problem. The idea is actually very simple. I have a table containing items, with a date column. Now I want to select all items from this database that have a date of today, or before (i.e. today or in the past). In my current implementation I store dates as integers, since most people seem to agree that that is the way to go.

Below is the (simplified) code for inserting an item.

Calendar calendar = GregorianCalendar.getInstance();
calendar.set(Calendar.HOUR_OF_DAY, 0); // Might not be necessary
calendar.add(Calendar.DAY_OF_YEAR, 4); // Today plus 4 days

SQLiteDatabase db = dbOpenHelper.getWritableDatabase();
ContentValues values = new ContentValues();
values.put(COLUMN_DATE, calendar.getTimeInMillis()); // Today as integer/long
long id = db.insert(TABLE_ITEMS, null, values); // Add to db

And next I want to select the items where the date is equal to or lower than today:

SQLiteDatabase db = dbOpenHelper.getReadableDatabase();
String[] columns = new String[]{COLUMN_ID, COLUMN_TEXT, COLUMN_DATE};
String[] selectArg = new String[]{"date('now')"};
Cursor cItems = db.query(TABLE_ITEMS, columns, COLUMN_DATE + "<= ?", selectArg, null, null, null);
//Cursor cItems = db.query(TABLE_ITEMS, columns, "strftime('%Y-%m-%d'," + COLUMN_DATE + ")" + select, selectArg, null, null, null);
//Cursor cItems = db.query(TABLE_ITEMS, columns, "date(" + COLUMN_DATE + ")" + select, selectArg, null, null, null);

Now all rows are selected, also the rows with a date in the future. Could anyone tell me what I need to do differently?

Thanks in advance!