Many people don't understand that the founders and their successors valued liberty over equality. Various presidents from George Washington all the way up to Cleveland generally adopted this view and the government was looked upon as something to protect people from more than something to help people.
The landscape however had been changing for a while. By the 1880's, people had been leaving their farms and small businesses for factory jobs in the city for decades. While citizens would not generally petition the government to increase their wages or maximize the hours they're required to put in on the job when they actually own the business they're working at, all that changed when the majority of Americans started to work for other people.
For some time, movements had been popping up that favored the interests of labor over capital. 'Free Silver' or the devaluation of U.S. currency had been pushed for a while as a means for the government to bail people out of debt and the movement to give pensions to Civil War veterans had been going on since before Cleveland took office.
In addition, there were immigrants pouring into the country from less stable places in Europe that advocated new and liberal ideas like socialism and anarchism.
Cleveland however continued to hold the view that the government did not exist to provide a safety net for people or create a more equal society. In his first term in 1885, his opposition to new social programs and refusal to have the government intervene in the private economy was not seen as major issue. Although he lost his bid for re-election, it was not because of popular anger at his economic policies.
However, when he was re-elected for a non-consecutive term in 1893, the country was in an economic crisis. Although this crisis was brought on by the 'free silver' policies that he had always been opposed to, he still took the blame for the crisis, or at least for not doing more to fix it. With many Americans out of work, his insistence on restricting government jobs and political appointments stood in direct opposition to the labor forces that were becoming stronger with every passing year.
As the depression continued, Cleveland's refusal to implement some kind of FDR type 'job creation' policy makes him seem out of touch to modern day historians. I think that this is unfair though since he was simply carrying out the widely held view of what government should and should not do that had been in place for more than one hundred years.