Rubuta ci gaba ga wannan sakin layi - Budaj ya rubuta ta Colorado Avalanche a cikin shirin 2001
a matsayin zabin farko na Avalanche kuma na 63rd gaba daya. Ya sanya lamba 31 don Avalanche bayan ya buga wa Hershey Bears na Ƙungiyar Hockey ta Amurka (AHL) da Toronto St. Michael's Majors na Ƙungiyar Hockey ta Ontario (OHL).