WASHINGTON — The chairman of the Federal Reserve, Ben Bernanke, said on Monday that he supported a second round of additional spending measures to help stimulate the economy.“With the economy likely to be weak for several quarters, and with some risk of a protracted slowdown, consideration of a fiscal package by the Congress at this juncture is appropriate,” Bernanke told the House Budget Committee.His remarks were his first endorsement of another round of energizing stimulus, which Democrats on Capitol Hill have advocated and Republicans have resisted.The White House, which flatly opposed a second stimulus package championed by House Democrats last month, said on Monday that President Bush was open to proposals. But aides to Bush still expressed skepticism about Democratic ideas that had surfaced so far.“We’re open to ideas and we’ll take a look at what comes our way,” Dana Perino, Bush’s press secretary, said aboard Air Force One as the president was flying to a business gathering in Alexandria, La. “What we’ve seen put forward so far, by the leaders in Congress, the Democrats, were elements of a package that we did not think would actually stimulate the economy.”Still, Bernanke’s testimony strengthened the hand of Democrats, who are pushing for a package of spending that could total $150 billion to $300 billion.Democratic leaders would like to pass a spending bill in a lame-duck session of Congress immediately after the elections on Nov. 4. But if Democrats cannot prevent Bush from vetoing a bill, they will most likely wait until the next president takes office in January.To draw in the White House as well as Republican lawmakers, Democrats are casting around for measures that Bush has wanted. One possible inducement could be passing a long-stalled free-trade agreement with Colombia. Republicans are also pushing for additional tax cuts.An earlier stimulus package, in which the government mailed out almost $100 billion in tax rebates during the spring and summer, provided a temporary lift to incomes and consumer spending. But the lift faded by late summer. Republican House lawmakers warned that they were likely to fight a new stimulus bill if it relied on spending.