In a vote of 223-203, the House fell short of the two-thirds majority needed to proceed. Although he has said he supports the wage hike and tax relief measures, Bush vetoed the bill for tying military funding with benchmark dates for withdrawing U.S. troops from the region.
"It makes no sense to tell the enemy when you plan to start withdrawing," Bush said in a nationally televised address on Tuesday. "All the terrorists would have to do is mark their calendars and gather their strength."
After the House vote Wednesday, leaders from both parties met with the president at the White House to begin negotiations for a second spending bill, which lawmakers expect to approve within a few weeks.
Rep. Steny Hoyer (D-Md.), the House majority leader, said he expects the new bill will include the minimum-wage hike and tax breaks.
Alternatively, Congress could also resend the wage and tax relief package as a standalone bill, or attached to a separate piece of legislation.
Under the current package, the federal minimum wage would be increased from $5.15 to $7.25 an hour over the next two years, and be offset by tax relief measures for smaller businesses over the next 10 years.
House and Senate Democrats made the wage hike a key legislative initiative after taking control of the Congress late last year.