from selenium import webdriver
from selenium.webdriver.common.by import By
from selenium.common.exceptions import StaleElementReferenceException, TimeoutException
from selenium.webdriver.support.ui import WebDriverWait
from selenium.webdriver.support import expected_conditions as EC
from bs4 import BeautifulSoup
import urllib,requests,unidecode,lxml,pdb
from pyvirtualdisplay import Display
from xvfbwrapper import Xvfb
class wait_for_more_than_n_elements_to_be_present(object):
    def __init__(self, locator, count):
        self.locator = locator
        self.count = count

    def __call__(self, driver):
        try:
            elements = EC._find_elements(driver, self.locator)
            return len(elements) > self.count
        except StaleElementReferenceException:
            return False

def return_html_code(url):
    print url #added in edit 1
    vdisplay =Xvfb()
    vdisplay.start()
    driver = webdriver.Firefox()
    driver.maximize_window()
    driver.get(url)
    # initial wait for the tweets to load
    wait = WebDriverWait(driver, 240)
    wait.until(EC.visibility_of_element_located((By.CSS_SELECTOR, "li[data-item-id]")))
    # scroll down to the last tweet until there is no more tweets loaded
    while True:
        tweets = driver.find_elements_by_css_selector("li[data-item-id]")
        print len(tweets)  #added in edit 1
        driver.execute_script("arguments[0].scrollIntoView(true);", tweets[-1])
        try:
            wait.until(wait_for_more_than_n_elements_to_be_present((By.CSS_SELECTOR, "li[data-item-id]"), number_of_tweets))
        except TimeoutException:
            break
     html_full_source=driver.page_source
     driver.close()
     vdisplay.stop()
     html_full=return_html_code(url)

Resultado:

https://twitter.com/search?q=Error%20Check&src=typd&lang=en
20
39
56
74

Eu tenho o código acima para rolar infinitamente uma página no modo infinito. Mas de alguma forma parece parar antes. Referências-https://stackoverflow.com/a/31058403/3646408

Editar 1:

$ phantomjs --version
2.1.1

No código runnning @alexce, ele mostrou uma saída diferente em 2 execuções, a verificação da data deixa claro que há mais tweets:

https://twitter.com/search?q=Error%20Check&src=typd&lang=en
20
40
59
76
95
114
133
152
171
191
211
231
249
267
Date of most old tweet: 12 Jan 2016


https://twitter.com/search?q=Error%20Check&src=typd&lang=en
20
40
59
76
95
114
133
152
171
191
211
231
249
267
287
303
317
337
356
373
388
400
418
437
457
476
492
Date of most old tweet: 8 Jan 2016

Edit2:

On runnning versão atualizada do código de @ alexce. Ele mostrou o erro abaixo após ~ 7000 tweets.

    Traceback (most recent call last):
      File "twitter_script.py", line 82, in <module>
        search_twitter('Alcoholics Anonymous')
      File "twitter_script.py", line 76, in search_twitter
        db_name=write_data_to_db(*get_twitter_data(query))
      File "twitter_script.py", line 24, in get_twitter_data
        html_full=return_html_code(url)
      File "c:\Users\sony\Desktop\social_network_extract_old\social_network_extract\scrollDownHtmlCode.py", line 48, in return_html_code
        html_full_source=driver.page_source
      File "c:\Anaconda\lib\site-packages\selenium\webdriver\remote\webdriver.py", line 464, in page_source
        return self.execute(Command.GET_PAGE_SOURCE)['value']
      File "c:\Anaconda\lib\site-packages\selenium\webdriver\remote\webdriver.py", line 199, in execute
        response = self.command_executor.execute(driver_command, params)
      File "c:\Anaconda\lib\site-packages\selenium\webdriver\remote\remote_connection.py", line 395, in execute
        return self._request(command_info[0], url, body=data)
      File "c:\Anaconda\lib\site-packages\selenium\webdriver\remote\remote_connection.py", line 463, in _request
        resp = opener.open(request, timeout=self._timeout)
      File "c:\Anaconda\lib\urllib2.py", line 431, in open
        response = self._open(req, data)
      File "c:\Anaconda\lib\urllib2.py", line 449, in _open
        '_open', req)
      File "c:\Anaconda\lib\urllib2.py", line 409, in _call_chain
        result = func(*args)
      File "c:\Anaconda\lib\urllib2.py", line 1227, in http_open
        return self.do_open(httplib.HTTPConnection, req)
      File "c:\Anaconda\lib\urllib2.py", line 1200, in do_open
        r = h.getresponse(buffering=True)
      File "c:\Anaconda\lib\httplib.py", line 1136, in getresponse
        response.begin()
      File "c:\Anaconda\lib\httplib.py", line 453, in begin
        version, status, reason = self._read_status()
      File "c:\Anaconda\lib\httplib.py", line 409, in _read_status
        line = self.fp.readline(_MAXLINE + 1)
      File "c:\Anaconda\lib\socket.py", line 480, in readline
        data = self._sock.recv(self._rbufsize)
    socket.error: [Errno 10054] An existing connection was forcibly closed by the remote host

Edit 3: Tentando o mesmo código para diferentes URLs.

https://twitter.com/search?q=Alcoholics%20Anonymous%20Drunk%20since%3A2006-03-24%20until%3A2006-04-23&src=typd&lang=en
Traceback (most recent call last):
  File "twitter_script.py", line 64, in <module>
    search_twitter('Alcoholics Anonymous Drunk')
  File "twitter_script.py", line 58, in search_twitter
    db_name=write_data_to_db(*get_twitter_data(query))
  File "twitter_script.py", line 31, in get_twitter_data
    html_full=return_html_code(url)
  File "c:\Users\sony\Desktop\social_network_extract_old\social_network_extract\scrollDownHtmlCode.py", line 30, in return_html_code
    wait.until(EC.visibility_of_element_located((By.CSS_SELECTOR, "li[data-item-id]")))
  File "c:\Anaconda\lib\site-packages\selenium\webdriver\support\wait.py", line 80, in until
    raise TimeoutException(message, screen, stacktrace)
selenium.common.exceptions.TimeoutException: Message:
Screenshot: available via screen

Edição 4:

ubuntu@ip-172-31-38-123:~/social_network_extract_proxy$ cat error.txt 
Traceback (most recent call last):
  File "twitter_script.py", line 70, in <module>
    search_twitter('alcoholics anonymous')
  File "twitter_script.py", line 64, in search_twitter
    db_name=write_data_to_db(*get_twitter_data(query))
  File "twitter_script.py", line 37, in get_twitter_data
    html_full=return_html_code(url)
  File "/home/ubuntu/social_network_extract_proxy/firefox_driver_code.py", line 35, in return_html_code
    driver=webdriver.Firefox(firefox_profile=profile)
  File "/home/ubuntu/anaconda2/lib/python2.7/site-packages/selenium/webdriver/firefox/webdriver.py", line 79, in __init__
    self.binary, timeout),
  File "/home/ubuntu/anaconda2/lib/python2.7/site-packages/selenium/webdriver/firefox/extension_connection.py", line 49, in __init__
    self.binary.launch_browser(self.profile)
  File "/home/ubuntu/anaconda2/lib/python2.7/site-packages/selenium/webdriver/firefox/firefox_binary.py", line 68, in launch_browser
    self._wait_until_connectable()
  File "/home/ubuntu/anaconda2/lib/python2.7/site-packages/selenium/webdriver/firefox/firefox_binary.py", line 106, in _wait_until_connectable
    % (self.profile.path))
selenium.common.exceptions.WebDriverException: Message: Can't load the profile. Profile Dir: /tmp/tmpvFoPrE If you specified a log_file in the FirefoxBinary constructor, check it for details.

Obteve o erro acima após um tempo.