WASHINGTON — President Obama on Friday announced an aggressive campaign to shrink the size of the federal government, a proposal less notable for its goal — the fight against bloat has been embraced by every modern-day president — than for the political challenge it poses to a hostile Congress.

Mr. Obama called on lawmakers to grant him broad new powers to propose mergers of agencies, which Congress would then have to approve or reject in an up-or-down vote. If granted the authority, he said, he would begin pruning by folding the Small Business Administration and five other trade and business agencies into a single agency that would replace the Commerce Department.

The White House estimated that the consolidation would save $3 billion over 10 years and result in reductions of 1,000 to 2,000 jobs. The savings is a mere rounding error in the $3.7 trillion annual budget, but the numbers may be less important than the message that Mr. Obama wants to cut wasteful spending.

“No business or nonprofit leader would allow this kind of duplication or unnecessary complexity in their operations,” Mr. Obama said to an audience of small business owners at the White House. “You wouldn’t do it when you’re thinking about your businesses, so why is it O.K. for our government? It’s not.”