Poland's lawmakers began a heated debate about the controversial dra.
Since being elected in 2015, the nationalist Law and Justice (PiS) party has tightened government control over courts and prosecutors, as well as state media.
The sanction has never been imposed before and would strip Poland of its voting rights at European Union summits.
Legislation puts Warsaw on collision course with European Commission.
Timmermans said Brussels would open a fresh legal case next week over the court laws, as well as giving Warsaw more recommendations on how to rein in the changes. The president will handpick the new composition of the court, although his decision will require a sign-off from the justice minister. Duda wants it to be a three-fifths majority.
The separation of powers between executive and judiciary is a fundamental democratic principle in the European Union, though in many member states the effectiveness of separation can be as much a matter of political culture as of formal structures.
Poland's president sought on Tuesday to end a bitter political conflict surrounding changes that the ruling populist party is introducing into the nation's judicial system. Another amends the rules of the common law courts, whose chairs shall be appointed by the minister of Justice.
In passing laws that observers say subjugates the Supreme Court and the judicial branch to the whims of politicians, Poland's government ignored a fresh warning from Brussels.
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The measure sparked critics' fears that Poland is shifting away from being a Western democracy, and opposition-backed demonstrations were planned across the country on Thursday night.
The European Commission warned Poland Wednesday that it could impose unprecedented sanctions if the country moves forward with plans to reform its judicial system.
Budka also condemned the speed with which the vote was handled, without proper public consultation.
"This is a very serious problem for Europe in terms of how it handles internal deviation from what had seemed to be a very strong consensus and agreement on respect for the rule of law", Saman Zia-Zarifi, the head of International Commission of Jurists, a Geneva-based body which defends the rule of law.
Opponents of the Polish government are protesting in front of the parliament building in Warsaw after the adoption of a bill that gives the president control over the Supreme Court instead of judges.
Protesters were kicking the metal barriers that separate them from the parliament and chanting "Shame". Some carried banners Thursday urging President Andrzej Duda to veto the bill.
The bill, submitted by the conservative ruling Law and Justice (PiS) party, must now be approved by the upper house.
The current judges could theoretically be reinstated in the revamped court, but there is little likelihood PiS will proceed in that fashion.
Tensions could be felt in Poland's parliament Wednesday night, where a debate over the bill culminated with a futile fight for the chairman's microphone and opposition deputies singing the national anthem as deputies from the ruling party rejected 1,300 proposed amendments in one vote.