Nowhere does any text describe Pompey's sole consulship of January 52 as introducing "martial law." Roman law had no such concept, at least not formally. The texts describe the proceedings surrounding Pompey's establishment as sole consul. The elections, which had been delayed, could not take place during the turmoil in the city, and by SCU the senate resolved to force the consular elections. Asconius tells us that the content of the SCU was to empower the interreges, tribunes, and Pompey (who was then a proconsul) to act "ne quid detrimenti re publica caperet" (so the state did not suffer harm"). A further clause of the SCU, says Asconius, empowered Pompey specifically to raise troops throughout Italy, an action that Pompey, with his extensive network of Italian clients, had in the past proven unmatched at, entering the city with troops almost immediately. Pompey was not in fact confirmed sole consul until late February and immediately moved to pass by SC two measures, one de vi and another de ambitu--these two SCs (which Asconius later calls leges, so they were probably carried to the comitia later) were especially harsh, imposing strict penalties and a new form of unequal trial. Pompey successfully combated the tribune Caelius' veto with the threat of force, compelling Caelius to back down.

Pompey's troops are no great mystery. Apart from the troops Asconius says he raised with the mandate of the SCU, Pompey had had military forces in Italy for two years already by January of 52. Pompey's proconsular command, extraordinarily including all of Spain and the province of Africa, had come along with four legions. Two of these legions (according to Plutarch) were loaned to Caesar in Gaul. Unlike Crassus, Pompey did not depart for his provinces and governed by proxy, which means that he exercised his proconsular power within Italy itself--meetings of the senate had to take place outside the pomerium to allow Pompey to attend. The supposed prohibition against maintaining troops in Italy is not something that really appears in the record at all before 49, and if it did exist in Roman imagination earlier Pompey had violated it many times before, though he pointedly disbanded his troops when he arrived in Italy at the end of the Mithridatic War.

So Roman politics in the 50's BCE were bad

The 50s were not, in fact, especially unusual. The teleological argument that the 50s necessarily led to the civil war because the socio-political situation was unstable is as flawed as saying that the Social War was an inevitable consequence of Livius Drusus' death in 91. Cicero gives us the impression that the 50s were an unusually violent and divisive time, but sources like Appian don't find it especially remarkable at all--Clodius, for example, dominates Cicero's writings during the decade but is included in only eight chapters of Appian, hardly more than a footnote. Plutarch finds Clodius' death so utterly unremarkable that he doesn't even mention it in the life of Pompey, and in his Cicero he misunderstands Cicero's apprehension while delivering his defense of Milo as being caused by the unnerving presence of Pompey's troops, not the threat of popular violence. Certainly something was going on in the 50s--the existence of the triumvirs is enough to show that--but if we disregard Cicero for a moment the violence and political division of the decade is presented as nothing especially new in the other sources. The Roman world had been dealing with this since 133 at the latest, and there were similar crises going all the way back to the Conflict of the Orders.