Evans, the council's most ardent stadium supporter, said he believes that the legislation will pass on the second vote "by a larger margin."
Baseball Executive Vice President John McHale Jr. said the league wanted to review the legislation before commenting. Although baseball officials named the Nationals last week and put season tickets on sale, the owners have not formally voted to relocate the team from Montreal to Washington. That vote could come this week.

D.C. Council member Harold Brazil (D-At Large) congratulates Mayor Anthony A. Williams after the stadium vote. Williams postponed a trip and sat through nearly four hours of the hearing "to show how important this is for the city." Story, Page B1.
(Michael Robinson-chavez -- The Washington Post)
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The D.C. Council's action comes after two months of debate among civic activists, business leaders and residents over whether to spend hundreds of millions of public dollars to build the stadium. Stadium detractors said public funds would be better spent on more pressing needs, such as libraries and schools. Supporters said a new stadium would spur economic development that would generate additional money for city projects.
Williams had lined up seven council supporters early last month by adding a community investment fund that included the $45 million for libraries, $30 million for other projects and up to $450 million in future bonds that would go to neighborhood needs.
But Cropp delayed a vote early last month, saying she was concerned about potential rising costs for businesses that would have to pay for the stadium. By eliminating the library fund, the council reduced the amount businesses will have to pay in the gross receipts taxes, Cropp said.
Graham, who had initially supported the stadium plan because of the library fund, was outraged yesterday.
"The most frequently heard comment I've heard is that there are more important and pressing needs than using public funds to finance a baseball stadium," Graham said. "Now I'm told that the only reason that attracts many of us to the legislation, addressing a compelling public need, is being taken out? There's nothing left. There's nothing here except a bad deal for the people."
Williams and his allies contested that characterization, saying the legislation still contains significant community investment. For one thing, the bill would establish a special district in neighborhoods around the stadium in which taxes from businesses would be designated to pay for bonds that could bring as much as $450 million for community programs, mayoral aides have said.
Mark Tuohey, chairman of the D.C. Sports and Entertainment Commission, said Major League Baseball has agreed to provide a $100,000 grant for the renovation of several youth baseball fields in the District by summer.
"The community benefits package is going to be very concrete and very real," Tuohey said.
Staff writers Thomas Heath and Lori Montgomery contributed to this report.