Opponents of the treaties argue that joining the bailout fund and debt pact for the 17 countries that use the euro would impose limits on the German Parliament's constitutional power to say how taxpayer money is spent.
Parliament ratified the treaties June 29 but President Joachim Gauck has held off signing them into law while the court hears the objections.
The Federal constitutional Court is being asked to issue a temporary order blocking Gauck from signing while it fully considers the case, which court officials have said could take several weeks. A decision on the injunction is also not expected Tuesday.
Under the treaties, Germany would join the European Stability Mechanism, a bailout fund for troubled eurozone countries backed by taxpayers' money. It would also adopt the new EU fiscal compact, under which 25 countries agree to write strict debt limits into national laws.
Some of the treaties' opponents argue that by joining the ESM, German taxpayers will be committed to paying for bailouts without Parliament's being unable to decide on spending. Members of the ex-communist Left Party argue that the debt treaty potentially binds the government to austerity imposed by the European Commission that would cut funding for social programs.
The court proceedings have hit Chancellor Angela Merkel's hopes of getting both treaties ratified and enforced quickly. They are key parts of eurozone leaders' recent efforts to build confidence in Europe's 17-member monetary union and get a handle on the euro's debt and economic crisis.
The Federal constitutional Court has typically been willing to approval measures deepening Germany's integration into the European Union, but has in the past imposed additional requirements to consult with Parliament on bailout measures.
Germany's Finance Minister Wolfgang Schaeuble is expected to appear and argue in favour of the treaties before the eight-judge panel.