The White House on Thursday rejected a Nicaraguan Contra aid plan proposed by Senate Democrats, but continued consultations with congressional leaders in an effort to secure additional assistance for the rebels. Colin Powell, President Reagan's national security adviser, went to Capitol Hill to meet with Senate Republican leader Robert Dole of Kansas to discuss Dole's alternative aid bill, which would include $20 million in new arms for the guerrillas, and the Democrats' plan. After three days of internal bargaining, Senate Democratic leader Robert Byrd of West Virginia announced Wednesday the $27 million plan for non-lethal U.S. aid to the rebels. But it offers no new money for weapons, the key point of opposition by the White House and Dole.