The Abbott government will hope to get its controversial metadata laws passed by the Senate on Thursday.
The coalition wants the laws, which would require telecommunication companies to keep consumer's metadata for two years, passed by the end of the week.
Senators stayed back late on Wednesday night to consider the changes, which Attorney-General George Brandis argues are crucial for police and intelligence agencies to thwart terror attacks.
Liberal Democrats senator David Leyonhjelm, independent Nick Xenophon and the Greens all want tougher privacy safeguards.
The laws passed the House of Representatives with bipartisan support last week after the government and Labor reached a deal on amendments to better protect journalists.
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