https://www.orange.sk/ is served by an Oracle HTTPS server, and works
with firefox or opera but not urllib2.

code snippet:

--------
import cookiejar
import urllib2

cookiejar = cookielib.LWPCookieJar()
opener = urllib2.build_opener(urllib2.HTTPCookieProcessor(cookiejar))
url = 'https://www.orange.sk/'
req = urllib2.Request(url, None)
s=opener.open(req)
-------- 

Here's some output with debuglevel=1 :

>>> opener.open(urllib2.Request('http://www.orange.sk/', None, headers))

reply: 'HTTP/1.1 200 OK\r\n'
header: Date: Mon, 19 Jan 2009 21:44:03 GMT
header: Server: Oracle-Application-Server-10g/10.1.3.1.0 Oracle-HTTP-
Server
header: Set-Cookie:
JSESSIONID=0a19055a30d630c427bda71d4e26a37ca604b9f590dc.e3eNaNiRah4Pe3aSch8Sc3yOc40;
path=/web
header: Expires: Mon, 19 Jan 2009 21:44:13 GMT
header: Surrogate-Control: max-age="10"
header: Content-Type: text/html; charset=ISO-8859-2
header: X-Cache: MISS from www.orange.sk
header: Connection: close
header: Transfer-Encoding: chunked
<addinfourl at 137417292 whose fp = <socket._fileobject object at
0x831348c>>

>>> opener.open(urllib2.Request('https://www.orange.sk/', None, headers))

reply: ''
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python2.5/urllib2.py", line 381, in open
    response = self._open(req, data)
  File "/usr/lib/python2.5/urllib2.py", line 399, in _open
    '_open', req)
  File "/usr/lib/python2.5/urllib2.py", line 360, in _call_chain
    result = func(*args)
  File "/usr/lib/python2.5/urllib2.py", line 1115, in https_open
    return self.do_open(httplib.HTTPSConnection, req)
  File "/usr/lib/python2.5/urllib2.py", line 1080, in do_open
    r = h.getresponse()
  File "/usr/lib/python2.5/httplib.py", line 928, in getresponse
    response.begin()
  File "/usr/lib/python2.5/httplib.py", line 385, in begin
    version, status, reason = self._read_status()
  File "/usr/lib/python2.5/httplib.py", line 349, in _read_status
    raise BadStatusLine(line)
httplib.BadStatusLine 

As you can see the reply from the server seems empty (which results in
the BadStatusLine exception)

Confirmed in 2.5, cannot confirm on trunk. Needs confirmation on 2.6 and
3.x.

Works fine for me in 2.6 but fails as said by OP on 2.5.
(I came across this in the course of my work and am submitting a change
in a bug for the first time, pardon me if something is inappropriate :)

I used this modified codeblock:

----------
import cookielib
import urllib2

cookiejar = cookielib.LWPCookieJar()
opener = urllib2.build_opener(urllib2.HTTPCookieProcessor(cookiejar))
url = 'https://www.orange.sk/'
req = urllib2.Request(url, None)
s=opener.open(req)
print s.read();

-------------------

2.6 gives a complete HTML page but 2.5 raises httplib.BadStatusLine
exception.

This bug is not reproducible in trunk, py3k and is not reproducible in
py26 releases too. I tried to hunt down if any changes in the code-line
from py2.5 to py2.6 had effect on the behavior mention (BadStatusLine) ,
but don't see any. 

I am closing this as works for me.