You could read the href attribute from the next_page link and add it to your urls list (yes, you should change your tuple to a list). It could be something like this:
from twill.commands import *
from bs4 import BeautifulSoup
from urllib import urlopen
import urllib2
import urlparse
with open('urls.txt') as inf:
urls = [line.strip() for line in inf]
for url in urls:
try:
urllib2.urlopen(url)
except urllib2.HTTPError, e:
print e
site = urlopen(url)
soup = BeautifulSoup(site)
for td in soup.find_all('td', {'class': 'subjectCell'}):
print td.find('a').text
next_page = soup.find_all('a', {'class': 'nextlink'}):
if next_page:
next_page = next_page[0]
urls.append(urlparse.urljoin(url, next_page['href']))