The bill proposes cutting the salaries of lawmakers who fail to attend congressional sessions.
But when it was due to be discussed on Tuesday, so many Senators were absent there was no quorum.
A new session has been scheduled for Thursday.
The Senator who proposed the bill, Alfredo Rangel, said that he hoped lawmakers would attend this time.
"This bill is not against members of Congress, it's for the the good of Congress, against absenteeism and in favour of its legitimacy and efficiency," he said.
As well as fining absent lawmakers, the bill also proposes that members of Congress produce a doctor's note if they miss sessions due to sickness.
If the bill is passed, repeat offenders who miss six or more sessions without a valid reason will be stripped of their mandate.
Absenteeism is a serious problem among Colombia's politicians, with bills often failing because they are not discussed in the allotted time-frame due to a lack of quorum.
If the absenteeism bill is not discussed on Thursday, it too will fail.
A bill aiming to punish chronic absenteeism in Colombia's Congress is to get a second chance after it failed to make it past the first hurdle because not enough lawmakers showed up.