Adriana Lastra, the Socialist Party's vice general secretary, said Saturday that she was "convinced" an agreement will be reached.
The Socialists had said negotiations with United We Can were going nowhere until its leader, Pablo Iglesias, ceded on Friday to their demand to not seek a seat in the Cabinet.
Sánchez would still need other parties' support for an absolute majority of the 350-member Parliament on Tuesday.
If he fails, another vote would take place Thursday where the bar is lower and Sánchez would just need more "Yes" than "No" votes.
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