Hogan expected a breakthrough or at least a temporary fix from the meeting, both of which would be a positive turn of events.
IHS Global Insight Economist Diego Iscaro said Greece and the euro zone leaders should reach a deal that is "closer to what the EU is proposing rather than what the Greeks are proposing."
On Tuesday, German Finance Minister Wolfgang Schaeuble refuted speculation that the European Commission would be ready to extend Greece's bailout, which expires on Feb. 28.
Read MoreGreeks soften tone as Germans stand firm
The news sent the Dow Jones industrial average down to single-digit gains before the index recovered to close up about 140 points, at 17,868.76, with Pfizer and Coca-Cola leading gains. Caterpillar was the greatest laggard.
Save for a move by the ECB, Greek government debt will officially cease to be valid collateral for bank loans on Wednesday as well.
"This (discussion) is going to be pushed on and on and on," said Martin Schulz, head of PNC Capital Advisors' International Equity Fund. He said Greece would probably stay in the European Union.
To be sure, Maris Ogg, president at Tower Bridge Advisors, said that Greece's debt issues are several years old and that countries such as Greece and Italy were different enough from Germany that they would be better off economically if they left the European Union.
The once recent driver of U.S. markets, oil only moved the energy sector on Tuesday in the second-straight day that stocks moved opposite to movements in the commodity.
Crude oil futures settled down $2.84 at $50.02 a barrel on the New York Mercantile Exchange. Greek concerns sent U.S. stocks lower to close in the red on Monday, despite oil settling higher.