While the upper house approved the government's 109 billion Swiss franc ($120.82 billion) contribution to the rescue package, parliament's lower, and larger chamber, later rejected it.
Seeking a compromise, the upper house passed changes to the measure on Wednesday morning, which the lower house will vote on later in the day.
As they returned on Wednesday, the upper house passed changes, which include a proposal for Switzerland's federal government to draft an amendment to the country's Banking Act.
Its aim would be to reduce the risks posed by systemically relevant banks, such as Credit Suisse and UBS for Switzerland, by, for example, raising capital requirements and restricting bonuses.
A shotgun marriage which saw Credit Suisse taken over by rival UBS (UBSG.S) for 3 billion Swiss francs and propped up with more than 250 billion Swiss francs in guarantees and support has drawn widespread criticism.