Absolutely!

The Pact of Steel was far from being something the Italian public or even many in the fascist leadership were keen on. And opposition to the plan came from the very top of the Fascist Party.

The Pact of Steel was deeply unpopular in Italy and was the last in a string of policies of alignment with Germany which were not well received in Italy. The introduction of the Leggi Raziali in 1938, a key policy aimed at strengthening this alliance (although many historians argue Mussolini went ahead with racial laws without German pressures), was extremely unpopular in Italy. Although anti-Semitism was a problem, the Jewish community in Italy was very well integrated in society and attitudes towards Jews were arguably much better than in the rest of Europe at the time. A number of Jews also played a prominent role in Italian politics with this role continuing into the Fascist era; a number of members of the Gran Consiglio del Fascismo were Jewish and as of 1933 it is said that nearly 10% of the Italian Jewish population had membership of the Fascist Party. Overall, the Jewish situation in Italy pre-1938 was political rather than racial with support or opposition based on political reasons.

It's little surprise then that when the Leggi Raziali were announced and introduced in 1938, many were opposed to it. This included a number of high ranking fascists who often had it out in a quite brutal manner with the anti-Semitic faction of the Gran Consiglio. At a public level, anti-Semitism wasn't as much of an issue as elsewhere and there were sections of the public opinion that saw this as an attempt to bring Italy closer to Germany. The Fascist government actually went out of its way to try and distinguish itself from Nazi Germany, such was the perception of the Leggi Raziali being a German-inspired policy.

However, even Mussolini himself wasn't as enthusiastic about the alliance with Germany. On a number of occasions, Mussolini himself was very evasive of German offers of alliance. Going even further, relationship between the Italian ministers and their German counterparts were often tense. Things were not as smooth or as friendly as people are often led to believe; even at the time of the Pact of Steel, many in the Fascist government were openly opposed to it.

Depending on whether we accept the reliability of his diary, but the Italian Foreign Minister at the time (and Mussolini's son-in-law), Galeazzo Ciano, wrote this in his diary:

For me, the Italian tragedy began in 1939 when I went to Salzburg of my own initiative and suddenly found myself facing the cold cynical German determination to start the war. The Pact had been signed that May. I had always been against it and made sure that persistent German offers would remain unanswered for as long as possible. In my opinion, there was no reason for Italy to link its fate, come what may, to Nazi Germany. However, I was in favour of a policy of collaboration as in our geographical position we could and we should detest the presence of over 80 million Germans in the heart of Europe, but we can't ignore it.

The decision to sign the Pact was taken by Mussolini, quite suddenly, as I was in Milan meeting Ribbentrop. Some US newspapers reported that Ribbentrop had been met with hostility by the people of Milan and that this was evidence of the deterioration of Mussolini's standing. I received the strongly worded order to agree to German requests for an alliance, which I had left unanswered for over a year and which I was hoping to leave unanswered for much longer.

As I said, this needs to be taken with a pinch of salt as this was part of the introduction to the diaries and written as Galeazzo Ciano sat in a cell awaiting his execution for treason.

None the less, it does echo sentiments of betrayal as the Pact of Steel was signed on the understanding that Italy would not be ready for war for another three to four years yet Germany declared war on Poland less than four months later. And the population itself was less than thrilled at being pegged to the decisions and fate of Nazi Germany.

Pre-1943 Fascist Italy is not my strongest suit but I suspect that u/Klesk_vs_Xaero is likely to be a much better and informed source on this topic. Potentially even correct any errors on my part.