UPDATE 1-Merkel takes blows in Bundestag after Greek failure
* Steinbrueck issues warning on euro support, budget
* Merkel says hopes for Greece deal on Monday
* German chancellor favours step by step approach
* Berlin backs Greek debt buyback, rate cut on loans (Recasts with Merkel and Steinbrueck speeches, background)
By Noah Barkin
BERLIN, Nov 21 (Reuters) - Germany's Angela Merkel came under fire from opposition parties on Wednesday after failing to clinch a financing deal for Greece, with her main rival threatening to withdraw support for her euro policies and delay a budget vote in parliament.
The exchange between Social Democrat (SPD) challenger Peer Steinbrueck and the chancellor was one of the fiercest in months, underscoring how difficult it will be for her to secure Bundestag backing for her euro rescue course in the run-up to next year's election.
Until now Merkel has been able to count on the support of parties like the SPD and Greens to help push through controversial bailout votes in the lower house.
"If we get the impression we are being cheated, we won't come to the rescue anymore when you need our support," Steinbrueck warned in a speech to the chamber just before Merkel took the podium.
The parliamentary debate was supposed to be focused on the 2013 German budget, which is up for approval on Friday, but it was coloured by the failure of European governments to reach an aid deal for Greece at a marathon overnight meeting in Brussels.
After failing twice to clinch an agreement, euro zone finance ministers scheduled a third meeting next Monday where they will try to overcome stubborn differences with the IMF and ECB over how to put Greek debt on a sustainable path.
In closed-door meetings with lawmakers in her conservative party on Wednesday morning, Merkel once again ruled out accepting a so-called "haircut", or losses, on European loans to Greece.
Instead, Berlin is pushing for a solution under which Athens would receive new funds from Europe's EFSF bailout fund to buy back Greek debt held by private investors at a discount. Germany is also prepared to lower the interest rates Greece pays on its loans and consider stretching out maturities.
But even with these measures, Greece seems sure to miss a goal of reducing its debt pile to 120 percent of annual economic output by 2020. The IMF is insisting this goal be kept, while governments are open to pushing back the target date to 2022.
"I believe there are chances, one doesn't know for sure, but there are chances to get a solution on Monday," Merkel said in her speech in parliament.
STEP BY STEP
She made clear however, that she favoured a piecemeal "step by step" solution to Greece's and Europe's problems - an approach Steinbrueck and his opposition allies say is based on a cynical political calculus and will only raise the long-term costs of the crisis for German taxpayers.
"This coalition is only fighting with and for itself, it isn't dealing with the problems of this country and its citizens," Steinbrueck said. "If you need all your strength to keep your coalition together, at the expense of the country, then you all need to go into rehab."
He pressed Merkel to delay Friday's vote on the German budget until there was more clarity on Greece. Finance Minister Wolfgang Schaeuble rebuffed that suggestion, promising that new Greek aid measures would not affect the 2013 budget.
Despite the failure to reach a deal in Brussels, Schaeuble said he was confident the Bundestag would be able to hold a separate vote on Greek aid at the end of next week.
Like Merkel, he made clear that different countries could agree different solutions for Greece - a sign that the divide may simply be too big to agree a common stance among all euro members.
Merkel is riding high in the polls roughly 10 months before the election, with two in three Germans saying she is doing a good job and her Christian Democrats (CDU) roughly 10 percentage points ahead of the SPD.
But satisfaction with her government is low, in part because of her struggling coalition partners, the Free Democrats (FDP), who have seen their support plunge.
The euro crisis also remains a major threat. The opposition and some private economists accuse Merkel of delaying a lasting solution to Greece's woes in order to avoid having to take politically risky steps before the vote.
In her speech to parliament, she was greeted with loud jeers when she said: "This government is the most successful one since German reunification". (Additional reporting by Stephen Brown, Andreas Rinke, Gareth Jones, Madeline Chambers, Thorsten Severin; Writing by Noah Barkin; Editing by Peter Graff)