WASHINGTON — After months of sparring with President Obama in the heat of the campaign season, Chamber of Commerce executives came to the White House this week with a far more conciliatory tone, offering up suggestions to avert large budget cuts without having to raise taxes.

But Mr. Obama’s top advisers were not budging. There would be no deal on the federal budget deficit, they told chamber executives, without higher taxes, participants said. If there were doubts about the White House’s resolve, Mr. Obama met the chamber’s chief executive afterward for an unscheduled Oval Office chat about the showdown.

For the United States Chamber of Commerce, long the leading business voice in Washington, this month’s negotiations over the nation’s debt will be a key test of whether it can retain its influence and swagger in the capital even after a string of bruising political losses.

Many business leaders are looking to the chamber as a bulwark against the White House’s push for higher taxes, but it is unclear if the century-old association has the clout it once did. Other business groups seen as more open to tax increases have become players in the negotiations, exposing rifts in the private sector.