As long as the Roman Legions were Militia (i.e. Every Roman Citizen served and had to provide your own armor, if you could not afford armor you ended up in the Roman Navy) this was NOT a problem. Basically the Militia type legion and the Roman People were one and the same thus the Roman legions WERE not able or willing to march on Rome (Through you did have at least two time periods in Republican Rome where the Poor People left the city in a Strike till the Upper Classes gave them more rights).
The Militia based Roman Army is what defeated Hannibal and Conquered the Mediterranean world. Once that happen the Roman citizen Soldier wanted to go home and stay home (He would accept living as a Colonist in a Province but he still retain his rights as a Roman). The problem stated with the Third Punic War (Hannibal was defeated in the the Second Punic War). During the Third Punic War it became clear that the Roman Citizen Soldier did NOT believe he was fighting for ROme but instead fighting for the Wealth of the Upper Classes. Over the next 50 years (Roughly 146 BCE to 104 BCE) this became more and more the case. Roman Citizens were willing to fight for Rome and fight their wealthy elite BUT were NOT willing to beat up some Barbarian just to make some of Rome's Elite richer. In 104 BCE this came to a head when Marius was ordered to raise two Legions and defeat some Germans who were invading the Provence of France (Southern France). Marius raised his army by PAYING Roman Citizens to join his army and giving them Armor to fight. The economic Situation over the previous 100 years had seen the large impoverishment of the Roman lower classes thus this was an opportunity to fight and actually get something out of the War.
Marius than defeated the Germans with this mercenary Army WHO WERE LOYAL ONLY TO HIM NOT THE ROMAN STATE. Other Roman Senators quickly followed suite. The Militia Army remained but unequipped and untrained after 104 BCE it became less and less important as time went on. Marius was of the Reform party of Rome backing more rights to the lower classes. In this Marius was opposed by his fellow Senators who recruited Marius chief lieutenant to act for them. The Senate than striped Marius of his command (which he disbursed) and told Sulla to defeat an enemy attacking Greece. Sulla defeated that Enemy and than turned his army on Rome (Technically the Senate had ordered Sulla to turn his army over to Marius but Sulla refused and Marched on Rome).
In the Mean time Marius had died of old age which left his party leaderless. Sulla than moved in before the Command of the Roman Army opposing him could be made clear. Thus Sulla defeated Marius's Army and ordered all of Marius veterans killed. Sulla than ruled as the First Dictator for Life Rome Ever had.
Sulla ruled for ten years and than retired and died. Sulla was succeeded by the First Triumvirate of Caesar (Marius's nephew and Chief Priest of Rome), Pompey (Sulla's Chief Lieutenant) and Crassus (The Richest man in Rome at that time). This represented the chief means of News in Caesar (the Priest hood of Rome controlled the news of Rome, remember printing is 1400 years in the Future thus the only way to get any message out is through the Priests class) with the Military power of Pompey with the Money of Crassus (Notice who won out, not wealth, not military might but who controlled the media).
As had been the custom for 100 years Caesar had been Consul (The Executive of the Roman Republic, Rome had two) and than ruled a province of Rome for five years afterwords (In this position he was "Proconsul" i.e. after being a consul through by usage means a Ruling representative in a foreign land). Technically Caesar's Province of Rome was "Gaul" which under Roman rule included what is now Milan and Lombardy in addition to today's France. As Proconsul of Gaul Caesar had the right to move his army anywhere in "Gaul" including Northern Italy which was NOT Italy by Roman law but "Gaul".
The Southern Border to "Gaul" was the Rubicon River, thus when Caesar lead his Army across the Rubicon he was moving his army out of his province and into Italy proper, something no Roman General had done since Sulla.
Thus the answer to your question is when and who? The issue is marching on Rome with an Roman Army. Sulla did it in 82 BCE, Caesar did in in 49 BCE and Galba did it in 68 AD to overthrow Nero. No one had done it during the days of the Militia Army, but once you had that Mercenary army that army did as its paymasters commanded.
For more on this time period see:
http://history.boisestate.edu/westciv/romanrev/Marius (Through watch reading on Marius while his Nephew Caesar did finally rule decades after Marius's Death, the sources we have are from the people he politically OPPOSED so the spin to make him look bad is strong in all of these sources):
http://heraklia.fws1.com/contemporaries/marius/http://www.roman-empire.net/republic/marius-index.htmlMarius by Plutarch:
http://classics.mit.edu/Plutarch/c_marius.htmlCaesar:
http://heraklia.fws1.com/Sulla:
http://heraklia.fws1.com/contemporaries/sulla/Sulla by Plutarch:
http://ancienthistory.about.com/library/bl/bl_text_plutarch_sylla.htmPompey the Great:
http://www.csun.edu/~hcfll004/PompeyTheGreat.htmlhttp://heraklia.fws1.com/contemporaries/pompey/Galba:
http://www.roman-emperors.org/galba.htmList of Roman Emperors:
http://www.roman-emperors.org/impindex.htm