As stocks pushed higher Tuesday on hopes of a European bailout, the "Fast Money" traders debated whether this rally is sustainable.

Talk of proposals to leverage up the 440 billion euro bailout fund to multiply Europe's financial firepower lifted global stocks on Tuesday.

The Bundestag, Germany's federal legislative body, is expected to approve a widening of the scope of the European Financial Stability Facility to aid weak states and banks, agreed by European leaders in July. If the measure passes another vote on Thursday, a portion of the fund's money would be used to shore up European bank capital. Another portion would be used as seed money for a European Investment Bank, according to one European official.

"The bailout proposal creates a giant CDO squared at the core of the economic system," Brian Kelly, co-founder and managing member of Shelter Harbor Capital, wrote in a note to clients, adding its time to buy gold .

"With this particular plan, I think it's disastrous, but I think they should take the same amount of money and recapitalize the banks. That would be a much better way to do it," Kelly later said on "Halftime." "Let's just recapitalize the banks and move on."

Meanwhile, trader Joe Terranova called this nothing more than a short-covering rally. The situation in Europe had appeared to be an Armageddon-type scenario, but now, he thinks European leaders seemed unified in making sure things get fixed.

The ball is in Germany's court, trader Zachary Karabell said. Germany can stare Greece down and make an example out of them, but at this point, its fortune is tied to Greece. So Karabell thinks Germany has the political will to get a bailout through.

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Trader disclosure: On Sept. 27, 2011, the following stocks and commodities mentioned or intended to be mentioned on CNBC’s "Fast Money" were owned by the "Fast Money" traders; Joe Terranova: Terranova is long VRTS; Terranova is long OXY; Terranova is long HOS; Terranova is long OIH; Terranova is long CVI; Terranova is long AXP; Terranova is long EMC; Terranova is long WFM; Terranova is long AMZN; Terranova is long WFC; Terranova is long AAPL; Terranova is long IBM; Terranova is long Silver puts.
Zach Karabell: Karabell owns (JPM) and (GOOG). Jon Najarian: Najarian is long (AMZN) call spreads; Najarian is long (ANR) call spreads; Najarian is long (AAPL) call spreads; Najarian is long (NFLX) call spreads; Najarian is long (YHOO) call spreads; Najarian is long (X) call spreads; Najarian is long (WLT) call spreads; Najarian is long (CBOE); Najarian is long (CME); Najarian is long (CIGX).

JOE TERRANOVA
Terranova is Chief Market Strategist of Virtus Investment Partners, LTD
Virtus Investment Partners Owns More Than 1% Of (ABAX)
Virtus Investment Partners Owns More Than 1% Of Building Materials Holdings
Virtus Investment Partners Owns More Than 1% Of (CASS)
Virtus Investment Partners Owns More Than 1% Of (CSVI)
Virtus Investment Partners Owns More Than 1% Of (EXR)
Virtus Investment Partners Owns More Than 1% Of (KRC)
Virtus Investment Partners Owns More Than 1% Of (LHO)
Virtus Investment Partners Owns More Than 1% Of (NRCI)
Virtus Investment Partners Owns More Than 1% Of Sun Pharmaceutical Industries Ltd
Virtus Investment Partners Owns More Than 1% Of (RLI)
Virtus Investment Partners Owns More Than 1% Of (XLB)
Virtus Investment Partners Owns More Than 1% Of (XLV)
Virtus Investment Partners Owns More Than 1% Of (XLP)
Virtus Investment Partners Owns More Than 1% Of (XLE)
Virtus Investment Partners Owns More Than 1% Of (XLF)
Virtus Investment Partners Owns More Than 1% Of (XLI)
Virtus Investment Partners Owns More Than 1% Of (XLK)
Virtus Investment Partners Owns More Than 1% Of (XLU)
Virtus Investment Partners Owns More Than 1% Of (SUBK)
Virtus Investment Partners Owns More Than 1% Of (WDFC)
Virtus Investment Partners Owns More Than 1% Of (YDNT)
Virtus Investment Partners Owns More Than 1% Of Domino's Pizza UK & IRL PLC

ZACH KARABELL
Rivertwice Capital is short (XLF)

David Konrad
KBW expects to receive or intends to seek compensation for investment banking services from Citigroup, Goldman Sachs, Bank of America, JP Morgan and Morgan Stanley in the next three months.

Phil Streible
No Disclosures

CNBC.com with wires.