Orrego served as an aide at the parliamentary office of Roberto Basualdo during Basualdo's term as National Deputy from 2001 to 2005. In 2007, Orrego ran for the mayoralty of Santa Lucía, but lost to Aníbal Fuentes.[2] He ran again in 2011, this time winning against incumbent Fuentes.[3] He was re-elected in 2015.[4]
In the 2019 provincial election, Orrego ran for the governorship of San Juan Province, as the candidate of the Frente Con Vos and in alliance with Juntos por el Cambio. He received 32% of the vote, and lost to Sergio Uñac of the Justicialist Party, who received over 54% of the vote.[5] Just months later, in the 2019 legislative election, Orrego ran for a seat in the lower house of the National Congress, as the first candidate in the Juntos por el Cambio list. The list received 38.37% of the vote, and Orrego was elected.[6] He was succeeded in the Santa Lucía mayoralty by his brother, Juan José Orrego.[7]
As a national deputy, Orrego formed part of the parliamentary commissions on Mining, Constitutional Affairs, Commerce, Sports, Mercosur, and Foreign Affairs.[8] Orrego was an opponent of the legalization of abortion in Argentina, voting against the 2020 Voluntary Interruption of Pregnancy bill, which passed the Chamber and later went on to legalize abortion nationwide.[9] He would later introduce a failed bill to repeal the Voluntary Interruption of Pregnancy law.[10]
In 2021, he was subject to controversy when, during a parliamentary commission debate held through videoconference, he unwittingly turned his microphone on and was overheard insulting a legislative aide.[11][12]
