First; That happened because Argentina was fighting itself, with the countryside wanting to curbe the power of the capital and the capital wanting to unite the whole country. Lopez tried to capitalize on that OTL, and what happened is exactly what would happen on this timeline. The argentinians would unite themselves to fight the invader. It is very common for enemies to unite against a invader on such cases, and this is the perfect situation, in OTL Solano expected to ally with some local lords on northern Argentina and use them against the federal government, but the opposite happened. On this scenario the same thing would happen, the argentinians would rally behind Buenos aires and push back the Paraguayans..
The problems in this part is that the Argentinean Don´t support the central government, in fact this moment was used to launch another revolt, the so called Revolucion de los colorados (link in Spanish) in the province of Mendoza. And the Argentinean Troops don´t fight even if his province was in danger of occupations as was the Case in Desbande de Basualdo where 8.000 Argentinean soldiers levied in the Entre rios province, the one directly south the area occupied by Paraguay, refused to be send to fight against Paraguay, so much that a decimation was not enough, and the army ended being disbanded .
And after that they try again, and again the troops dessert in this case 6.000 horsemen in the
Desbande de Toledo
After that in 1867 the Argentinean centralist Government could stop all the rebellion(s) and send troops again against Paraguay, but in 1868 they have another Revolt This time in the Santa Fe Province and Another in the Corrientes Province, that ironically enough was the one recently liberate of the Paraguayan occupation.
The Argentinian troops would have a higher morale, agian, they are fighting a invader from the closest that America came from a totalitarian state on the 19th century and this state wants to take huge chunks of the Argentinian land. Argentina has a better economy and a larger population, so they will eventually win a war of attrition. There another point comes, however, Solano can use his numbers and win some decisive victories (taking large casualties in the process) and force the argentinians to surrender. This IS possible and this could have happened, but the Paraguayan army was already mobilized to it's max and they needed to demobilize, while the Argentinian army wasn't, and so as soon the paraguayans demobilize, the Argentinians will come to crush them and recover the lost land..
As i could demonstrate in my anterior point, the Argentinians don´t have the slightest interest in fight a war against Paraguay if they are send by the Centralist Government of Buenos Aires, as most of the troops levied to fight against Paraguay were occupied to stop the revolts inside the national Territory,or in some cases, rebelled themselves against being send to fight against Paraguay, by 1867 most of the troops Argentina field in the Paraguayan front where A) prisoners, B) captured Paraguayans Soldier) or C) mercenaries. and where barely more than 3.000 soldiers,
There is a reason the Lions share of the fight was done by Brazilian Troops
Brazil cannot support paraguay because Paraguay was friendly for the anti brazilian faction on the Uruguayan civil war.
Realpolitik, just because this guys don´t support me, does not mean i can´t help then when they are fighting my enemies, like the USA backed Taliban in Afghanistan fight against the USSR., the Molotov-Ribbentrop pact, French Backed Protestant Troops during the 30 years war, Examples Abound, you because just must not don´t mean you cannot