You might check the file sizes of the database where the backup has been taken from. If the backup had been compressed the size might be much more larger than you think.
These querys might give you some details about the file size and the usage.
SELECT
NAME,
TYPE_DESC,
(SIZE * 8) / 1024 [Size in MB],
PHYSICAL_NAME
FROM SYS.DATABASE_FILES;
SELECT (SELECT
SUM(size)
FROM sys.database_files
WHERE type IN (0, 2, 4))
* 8 / 1024 AS [Database size in MB],
SUM(allocation_units.total_pages)
* 8 / 1024 AS [Space used in MB],
(SELECT
SUM(size)
FROM sys.database_files
WHERE type IN (1, 3))
* 8 / 1024 AS [Log size in MB],
SUM(allocation_units.used_pages)
* 8 / 1024 AS [Log used in MB]
FROM sys.partitions
JOIN sys.allocation_units
ON partition_id = container_id;
Depending on the results you may reduce the file sizes before creating a backup. If you use the database temporary and do not rely on performance use a fast usb stick or external harddisk or even a network storage where you can restore the database for the case you are low on disk space. Don't forget to detach the database before removing the drive or disconnect from the network.