At stake are Brazil's lucrative trade and energy relations with landlocked Paraguay, a country less well off than economic dynamo Brazil but still an important market for Brazilian exports and partner in Itaipu Dam power generation.
Brazilian President Dilma Rousseff has come under fire from critics who question her handling of Brazilian-Paraguayan diplomacy after Lugo's removal June 22.
Franco's presidency is contested by Latin America's regional organizations but moves to have the country suspended from the Organization of American States failed, a blow to Rousseff's approval ratings.
Brazil joined Argentina and Uruguay in campaigning successfully for Paraguay's suspension from the Mercosur trade bloc and the Union of South American States. Both Mercosur and Unasur likened Lugo's speedy impeachment to a coup, an interpretation rejected by OAS.
To complicate matters for the Brazil-led campaign against Franco's regime, critics point out that Lugo did in fact accept the congressional vote that removed him from the presidency.
Critics say the diplomatic move is set to become an embarrassment for Rousseff, Argentine President Cristina Fernandez de Kirchner and Uruguay President Jose Mujica as Franco's presidency settles into power.
Diplomatic moves to have Paraguay's ties with the European Union suspended have also remained inconclusive, while the EU adopts a conciliatory position that it hopes will steer Paraguay to democratic elections next year.
The three presidents have courted controversy in the manner in which they used Paraguay's suspension to admit Venezuela to full membership of Mercosur.
Paraguay's legislature was the last hurdle in the way of Venezuela's membership of Mercosur. The country's suspension from the trade bloc cleared the way for Venezuela's Mercosur membership to be ratified.
Mujica said that "while it is true that the proposal was elaborated in the first place by Brazil, we three agree (the presidents of Argentina, Brazil and Uruguay) about Venezuela's entry in the bloc."
He said "the political will involved in the case, far exceeds the possible legal impediments regarding the matter."
Critics of the move aren't convinced, however, and in media comments have warned the diplomatic impasse created with Paraguay is could deepen divisions within the organization.
Mujica has further muddied the waters by calling for a merger of Mercosur and Unasur. Venezuelan President Hugo Chavez, in one of the first statements after Venezuela's admission to Mercosur, declared plans to galvanize Mercosur member countries into a defense pact.
Paraguay's new government has accused Chavez of financing moves to destabilize the country.
Argentine President Cristina Fernandez said the region will resist moves that went against popular will, a reference to the Paraguayan crisis.
"Let there be no confusion," Fernandez declared, "we are all united and we are all going to fight tooth and nail, not for governments, or persons, but for the will of the people freely expressed in open, democratic, transparent elections."
The Argentine leader said Mercosur, Unasur and other regional organizations "enabled the region to overcome difficult moments" in several countries.
A European Parliament mission on a fact-finding visit to Paraguay urged the new government to tone down the war of words and find ways of normalizing relations with neighbors.
Brazilian analysts also say a working relationship with Paraguay will be hard to avoid while the new government prepares for elections next year.
All three countries that campaigned against Paraguay stand to lose trade and other benefits if the current stand-off continues.