When the unification movement started, Cavour only wanted Piedmont to annex what was North of Rome. He practiced Realpolitik, which meant he was interested in tangible results and all of his actions were calculated. Garibaldi, a Romantic Italian, wanted unity for all of Italy. Garibaldi sent his army of Red Shirts to the Southern tip of Italy and they fought towards the North. Everywhere they went, the people asked to be annexed by Piedmont. He annexed all these lands. When Garibaldi and Cavour met halfway through Italy, he figured he might as well compromise and take the southern lands. So in a way, there were people opposed to total unification. The Italian state later received help from the French to annex Venice from Austria and Rome from the Pope.

Source: Ronald R Palmer, A History of the Modern World.

If anyone wants to correct something, please do, it's been a while since I took Euro and I don't have time to look at my notes at the moment.

Same with /u/paxerz , there is a lot of depth to this depending on how one defines "unification". Historically there has been a common identity "Italy", however agreement as to how a united Italy should be like (and more importantly who should rule it) is a complicated subject.

Following the 1848 revolutions, the Kingdom of Sardinia allied with the Papal States and the Kingdom of Two Sicilies to attack Austria's Italian possessions in Piedmont and Tuscany. After initial success the Papal State backed out of the alliance for fear of Sardinian dominance in the continent, and the Austrians beat the Sardinians.

At the same time in 1849 a Roman Republic was declared in Rome, with Pope Pius IX fleeing the town. Although the republic was supported by activists such as Garibaldi, France and Spain sent troops to put the Pope back in power.

A decade later, Cavour the Prime Minister of Sardinia managed to gain French support through Napoleon III. With French help they were successful at first, but the French sought peace after just most of Lombardy was won. The Austrians still held Venice, and the two other powers of Italy -- Papal States and Naples -- were still independent. Further, Nice the home town of Garibaldi was given to the French.

A temporary weakness in Sicily, as their Swiss mercenaries were recalled back to Switzerland, allowed Garibaldi to seize power there, and then in the city Naples. Although the King of Naples fled the capital, Garibaldi couldn't dislodge him from entrenched positions, so he had to ally with Sardinia and give up on republican ambitions. Since Sardinian troops will have to cross Papal States territory, the Pope was agitated and threatened excommunication. In reply, Garibaldi outright threatened Rome, which led to Catholics worldwide to send money and even volunteer troops to Rome. The Sardinians marched south anyway, beat the Papal army, and then that of the Kingdom of Sardinia.

After all that, most of Italy was united, this time under Victor Emmanuel of Sardinia, except for Venice which was still under Austria.

To in summary, it took a long time for agreement of who should lead Italy, and what kind of country Italy should be. It took many negotiations, popular uprisings, and pragmatic alliances.