WASHINGTON — The Senate approved President Barack Obama’s giant economic stimulus measure on Tuesday, part of a string of powerful government steps that could marshal close to $3 trillion in taxpayer and private money to revive the collapsing national economy.

The 61-37 vote by the Senate was a key victory for the president but sets up difficult negotiations with the House, which passed a slightly different version than the $838 billion bill approved Tuesday.

Majority Leader Harry Reid, D-Nev., vowed to send a finished bill to Obama’s desk “as soon as possible.”

Obama, who was in Fort Myers, Fla., welcomed the vote as “good news. … It’s a good start.”

It came shortly after the Treasury Department and Federal Reserve moved to commit colossal sums of money to help thaw credit markets and slow layoffs that have left 3.6 million Americans unemployed.