"I encourage you to think about who you are hurting," the president said in the White House briefing room.
Obama's remarks came after the Senate, on a 54-44 party line vote, removed language defunding healthcare reform from a stopgap bill funding the government for 45 days and sent the legislation back to the House.
The Senate bill funds the federal government until mid-November and restores money for the Patient Protection and Affordable Care Act that House Republicans removed last week, leaving the two chambers on a collision course.
With a government shutdown looming Tuesday without a continuing resolution, the House Republican Conference will meet Saturday to decide its next move.
Speaker John Boehner, R-Ohio, has said an amended spending bill would not reach the House floor.
"My message to Congress is this: do not shut down the government, do not shut down the economy, pay our bills on time," Obama said at the White House.
He accused Republicans of "political grandstanding" with their demands.
"Past shutdowns have disrupted the economy, and this shutdown would as well," he said. "It would throw a wrench into the gears of our economy at a time when those gears have gained some traction. And that's why many Republican senators and many Republican governors have urged Republicans to knock it off, pass a budget and move on. Let's get this done."
Earlier, senators voted 79-to-19 -- with 25 Republicans voting in favor -- to end debate on the measure to fund the government and defund the Affordable Care Act, known as Obamacare. The vote on an amendment removing language defunding provisions of the healthcare law was a party line 54-44.
McConnell acknowledged Republicans needed five Democratic votes to defund the healthcare law while Reid spoke about the millions who will benefit from greater access to a doctor, telling a personal story about how a family friend drove him 50 miles to a hospital when he was a child for surgery that saved his life.
Meanwhile, federal workers were to learn who can and cannot work if Washington shuts down.
The Office of Management and Budget and the Office of Personnel Management said Thursday it would put their shutdown plans online Friday afternoon.
Supervisors will then tell employees if they can expect to be furloughed after Monday, the last day of the fiscal year, the National Treasury Employees Union said.
The final word on who works and who doesn't is expected to come early Tuesday if a stopgap measure to fund the government for 46 days is not passed in Congress and signed into law by then, the union said.
The possible government shutdown is one of two fiscal crises rattling lawmakers. The other is the federal debt limit, set to be reached in 20 days.
Treasury Secretary Jack Lew warned Congress Wednesday he would run out of emergency borrowing measures "no later than Oct. 17." Without the additional borrowing authority, the government's $30 billion cash on hand "would be far short of net expenditures on certain days, which can be as high as $60 billion," he said.
On Thursday, Obama repeated he wouldn't negotiate on the debt ceiling or sign any bill that defunds or delays the healthcare law.