Does he have to take money from his capital that he needs in order to do Hajj?

Hajj is not obligatory except for the one who is able to do
it, because Allaah says (interpretation of the meaning): “And Hajj
(pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to
Allaah, those who can afford the expenses (for one’s conveyance, provision
and residence)” [Aal ‘Imraan 3:97].  

What is meant by being financially able to do it is that one
has enough to cover his travel costs and his family’s expenses until he
returns and that he has enough after he returns to cover his expenses and
those of the people on whom he spends, such as rent from properties he own,
salaries, business and so on. Hence he is not obliged to do Hajj using the
capital with which he does business from which he spends the income on
himself and his family, as the reduction in the capital will result in the
reduction of the income which would then not be enough for him and his
family. 

Ibn Qudaamah (may Allaah have mercy on him) said in
al-Mughni (5/12): 

The one who has property that he needs for his dwelling, or
for his family’s dwelling, or he needs it to rent it out to cover his
expenses or those of his family, or trade goods that if their amount is
reduced then his profit will not be sufficient to cover his expenses, is not
obliged to do Hajj.  

The scholars of the Standing Committee for Issuing Fatwas
were asked:  

I am an Egyptian citizen and head of a family consisting of
two children and a wife, and my salary in Egypt is barely enough to cover
the necessities of life, and I do not have any other income. I worked in one
of the Gulf countries for four years, and I earned some money which I put in
an Islamic bank to provide me with an income that will help me to bear the
various burdens of life, so that my salary and this income will be
sufficient for me and my family to live a reasonable life. Am I obliged to
devote some of this money to the expenses of Hajj, and am I obliged to do
Hajj in these circumstances? Please note that if I take some money out of
this bank account to spend on Hajj, that will affect my monthly income and I
will encounter some financial difficulties.  

They replied: 

If your situation is as you described, then you are not
obliged to do Hajj, because you are not able to do it. Allaah says
(interpretation of the meaning): “And Hajj (pilgrimage to Makkah) to the
House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford
the expenses (for one’s conveyance, provision and residence)” [Aal ‘Imraan
3:97]. And He says (interpretation of the meaning): “So keep your
duty to Allaah and fear Him as much as you can”[al-Taghaabun 64:16] and
“and [Allaah] has not laid upon you in religion any hardship”[al-Hajj
22:78]. 

And Allaah is the Source of strength. May Allaah send
blessings and peace upon our Prophet Muhammad and his family and companions.
End quote. 

Standing Committee for Academic Research and Issuing Fatwas 

Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, Shaykh ‘Abd
al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allaah ibn Ghadyaan. 

Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah
wa’l-Ifta (11/35, 36). 

Based on this, you do not have to do Hajj, so long as you
need the money that you have for your expenses and those of your family.