Q:

Do long working hours in Spain affect birth rate? 

According to "Spain appoints 'minister for sex' to reverse nation's plummeting birth rate":

Experts say long working hours and a culture of eating late at night and going to bed after midnight are partly to blame for the nation’s sex famine. 
Rafael Puyol, of the IE Business School in Madrid, said: “They do not help with making a family.  Then when a child arrives it is even worse.” 

Is there evidence for the claimed causality? 

Claim part #1: Spain has long working hours (presumably, in comparison with other countries, in relation to birth or intercourse rates)

Claim part #2: there is causation between the two

A:

Hours Worked
First, Spain does not have excessively long hours of work among OECD countries. 
Source: OECD.Stat:

In fact, at 1,691 hours per annum in 2015, Spain is slightly below the median of 1,749 and mean of 1,756. 
Spain does not have longer working hours in comparison with other OECD countries
Long hours reduces birth rates
Lack of correlation is strong evidence of lack of causation.  Using the data above (averaged in 5 year blocks between 2000 and 2015) and cross referenced with UN data on crude birth rates gives:

(The graph is produced by averaging the hours worked from the OECD data set ito 2000-2005, 2005-2010 & 2010-2015 blocks to correspond with the UN data points, matching the data for each country and plotting as an x-Y scatter). 
There is a correlation, however, it is tiny (R2 = 0.1) and it is obvious from the look of the graph that there is a lot more noise than signal here.  Notwithstanding, it goes the wrong way, that is, longer hours are correlated with higher birth rates. 
A reduction in hours worked is not correlated with higher birth rates

