(Maintainer: I hope it is OK to post this possible solution here because it may be useful to others. Please feel free to close it as it is obviously a "resolved" issue that can affect your module.)

Scenario: You are using Node Import (in my case version: 6.x-1.x-dev) and you get stuck on Step 1, i.e., you select a Content Type and click Next and the screen just refreshes and stays on Step 1 (as reported previously: #684000: Cannot proceed beyond step 1), try this:

1) Check your log: /admin/reports/dblog
2) If you see: 

Warning: Table 'yourdrupaldb.cache_page' doesn't exist query: SELECT data, created, headers, expire, serialized FROM cache_form

Or, more specifically:

Table 'yourdrupaldb.cache_form' doesn't exist query: UPDATE cache_form SET data = 'a:9:{s:4:\"page\";s:4:\"type\";s:11:\"back_button\";s:4:\"Back\";s:13:\"reload_button\";s:11:\"Reload page\";s:12:\"reset_button\";s:10:\"Reset page\";s:2:\"op\";s:4:\"Next\";s:11:\"next_button\";s:4:\"Next\";s:13:\"form_build_id\";s:37:\"form-4d4a27ecfd90c576e7641315dae8af32\";s:10:\"form_token\";s:32:\"04441ba1a0d3e179961594c65760e44c\";s:7:\"form_id\";s:20:\"node_import_add_form\";}', created = 1310474203, expire = 1310495803, headers = '', serialized = 1 WHERE cid = 'storage_form-f2144a14845aaa5fca067d9616c85c72' in /var/www/yourwebpath/includes/cache.inc on line 109.

3) Try this solution: http://www.widwad.com/content/fix-for-drupal-warning-table-yourdrupaldbc...

I ran into this one when I dumped and re-loaded my Drupal MySQL databases for replication purposes and I wasn't replicating the cache tables (helps with the performance, you can see how here.) This solved it immediately and I could use Node Import again.

Hope it helps!