The relationship between Catullus and Caesar is a rocky, kind of resentful one, to put it kindly. There are two poems by Catullus (out of about 116) that directly attack Caesar—not necessarily as a politician, but in a very vitriolic ad hominem way, taking blows at his pride through his manhood. The first is a two-line dismissal of Caesar as not even worth Catullus’ time, and the second is an extended indictment of Caesar’s, er, sexual proclivities. The latter is a more direct attack, using baser language and alluding to Mamurra, one of Caesar’s political cronies, as more of a (cough) butt buddy.
The first one I mentioned is Catullus 93, which I’ve loosely translated below.
XCIII. ad Gaium Iulium Caesarem
Nil nimium studeo, Caesar, tibi velle placere,
nec scire utrum sis albus an ater homo.
I take no great pains to please you, Caesar, nor to know whether you are a white or a black man.
The white/black contrast has moral connotations as well, and the Latin word ater, aside from meaning “gloomy, dark, or lusterless” also has poetic usages meaning “malevolent,” etc. which contrast with albus; aside from meaning “white”, albus also means “favorable” or “propitious,” even before the shift in language (which happens gradually, but comes to fruition around 500 years later) that results in heavy moral connotations associated with many words which previously were in the common lexicon.
LVII. ad Gaium Iulium Caesarem
Pulchre convenit improbis cinaedis,
Mamurrae pathicoque Caesarique.
nec mirum: maculae pares utrisque,
urbana altera et illa Formiana,
impressae resident nec eluentur:
morbosi pariter, gemelli utrique,
uno in lecticulo erudituli ambo,
non hic quam ille magis vorax adulter,
rivales socii puellularum.
pulchre convenit improbis cinaedis.
This is the most obvious and well-fleshed-out attack on Caesar, and it roughly translates as follows:
Well-matched are the wanton sodomites, Mamurra and Caesar, f*ggots both. No wonder: Equal stains to each the other, one from city girls and the other from Formian, are impressed on them and cannot be washed out. Equally diseased, twins to each the other, both “experts” in one bed, neither a more voracious adulterer than the other—rivals of their “colleagues” and of little girls. Indeed, well-matched are these wanton sodomites.
I’ll leave it with a couple of bits from Spaeth’s article on Caesar’s political friends and enemies among Roman poets, which is cited in a lot of scholarship on Catullus.
Catullus used his poetic talents for passionate discourse on politics; there were active political participants among the Roman political scene at the time, as well, including some of the poetae novi, among whose numbers was Catullus himself. Along with common poetic ideals, the poetae novi exhibited similar political ideals, and “their changes of front in the face of political developments were not greatly different from those of Cicero himself, with whom…most of this group were on terms of close intimacy” (Spaeth, “Caesar’s Friends and Enemies Among the Poets, 541-2).
Caesar also allowed Clodius to “have his way with Cicero” in 58, and Clodius and Clodia (Lesbia, the lover who spurns Catullus) were by no means on Catullus’ good side by that point. He didn’t want to actively participate in the political scene, but he couldn’t just set aside his pride and entirely remove himself from politics, either. And so he joined “other young intellectuals of independent spirit in bitterly lampooning Caesar, Pompey, and their political henchmen” (Spaeth 545).
Tl;dr: Caesar realized that having a poet as a political enemy was not so good, Catullus had bitter basement emo hatred of Caesar