Question: Someone is short of time, for example, he awoke just before sunrise. He does not have time to perform Wudhu and Salaah. Can he make Tayammum? 

Answer; He may not. He must make Wudh. (If he is Junub he must make Ghusl.) He will  then perform Qadha Salaah after the sun has arisen the height of a spear. Lack of time is not a valid excuse for Tayammum. 

وكذلك ان ضاق الوقت فخشي ان توضأ فاته الوقت لم يتيمم ، ولكنه يتوضأ ويصلي فاءتته (القدوري ص٤٣)

And Allah Knows Best

Yusuf Moosagie