Galtieri and Anaya were so incredibly stupid they should have been executed for that. And so, they've 'planned' under the idea that the UK wouldn't fight back. Which is to say, little planning was actually done.
Any politician able to reach presidency will understand there is no way whoever is the British PM can not, under any circumstance, accept an armed invasion and thus, would plan accordingly.
And here comes the problem: The OP puts the war in the 1985-1990 timeframe, if not later. By then, the Argentine armed forces would have received the full lot of exocets and would have probably worked out the issues with the submarine torpedos. Proper planning would also mean the invasion would be carried at a time when the RN is at it's lower state of readiness, war is expected and the runway in the islands is prolonged so Mirage IIIs can operate from there. More preparations can be taken without drawing too much attention: figuring out how to take out missile frigates with bombs and modify them before hand, importing a couple of additional tankers and improve the conscripts training, for instance.
The RN was supposed to be undergoing cuts in one hand but, in the other, would already have, at least one more carrier and would probably have AEW Sea Kings as well (or were those developed as a consequence of the war?). So, overall, the aeronaval battles would have been far bloodier.
Now, let's assume a democratic president analyze the war plans with the Joint Chiefs of Staff and he's convinced there is a chance of defeating a British task force in the open oceans. He would also know the British PM can't back down, even then. So he should expect the British would get the Americans, with their far more powerful CVBGs, involved. And an intact Argentine aviation and submarine force can't take on them, let alone a bloodied and depleted one. Also, in the diplomatic front, there will be no lobby inside the American State Department to support Argentina, as the country is no longer fighting international communism/torturing Central American peasants on behalf of the CIA.
So, in short, I don't think a democratic president would go for it.