There's something missing before "was".
Let's presume we're missing the pronoun 'it', and divide up the sentence like this:
The government's assertion that it was over = subject
did little to reassure = verb phrase
the small businesses that were still struggling. = object
In other words, the government claimed that something - a recession or financial crisis of some kind - was finished. However, this assertion did not reassure the struggling businesses very much. These businesses suffered under the recession, and they were still struggling now, so the government's 'reassurances' did not convince them.