WASHINGTON — Internet shoppers are moving closer to paying sales taxes for their online purchases. But the fight is far from over.

The Senate voted 63-30 Thursday to advance a bill that would impose state and local sales taxes on purchases made over the Internet. An agreement among senators delayed the Senate’s final vote on passage until May 6, when senators return from a weeklong vacation.

Opponents hope senators hear from angry constituents over the next week, but they acknowledged they have a steep hill to climb to defeat the bill in the Senate.

Their best hope for stopping the bill may be in the House, where some Republicans consider it a tax increase. President Barack Obama supports the bill.

The bill would empower states to reach outside their borders and compel online retailers to collect state and local sales taxes for purchases made over the Internet. Under the bill, the sales taxes would be sent to the states where a shopper lives.

Under current law, states can only require stores to collect sales taxes if the store has a physical presence in the state. As a result, many online sales are essentially tax-free, giving Internet retailers an advantage over brick-and-mortar stores.

“We look forward to passing this landmark bill in 11 days and call on the House to stand up for America’s Main Street businesses with us,” Sen. Dick Durbin, D-Ill., said shortly after Thursday’s vote.

Senate Democratic leaders wanted to finish work on the bill this week, before leaving town for the recess. But they were blocked by a handful of senators from states without sales taxes.

Oregon, Montana, New Hampshire and Delaware have no sales taxes, though the two senators from Delaware support the bill.

“I think it’s going to be interesting for senators to get a response from constituents over this upcoming week,” said Sen. Ron Wyden, D-Ore. “I’m not sure that the country knows that something like this coerces businesses all around America to collect other people’s sales taxes.”

The bill pits brick-and-mortar stores like Wal-Mart against online services such as eBay. The National Retail Federation supports it. And Amazon.com, which initially fought efforts in some states to make it collect sales taxes, supports it, too.

Retailers who have lobbied in favor of the bill celebrated Thursday’s vote.

“The special treatment of big online businesses at the expense of retailers on Main Street will soon be a thing of the past,” said Bill Hughes of the Retail Industry Leaders Association. “The overwhelmingly bipartisan support for leveling the playing field is rare in today’s political environment and paves the way for a level playing field once and for all.”

Supporters say the bill is about fairness for local businesses that already collect sales taxes, and lost revenue for states. Opponents say the bill would impose complicated regulations on retailers and doesn’t have enough protections for small businesses. Businesses with less than $1 million a year in online sales would be exempt.

Many of the nation’s governors — Republicans and Democrats — have been lobbying the federal government for years for the authority to collect sales taxes from online sales.

The issue is getting bigger for states as more people make purchases online. Last year, Internet sales in the U.S. totaled $226 billion, up nearly 16 percent from the previous year, according to Commerce Department estimates.

The National Conference of State Legislatures estimates that states lost $23 billion last year because they couldn’t collect taxes on out-of-state sales.

Anti-tax groups have labeled the bill a tax increase. But it gets support from many Republicans who have pledged not to increase taxes. The bill’s main sponsor is Sen. Mike Enzi, a conservative Republican from Wyoming. He has worked closely with Durbin, a liberal Democrat.

Enzi and Durbin say the bill doesn’t raise taxes. Instead, they say, it gives states a mechanism to enforce current taxes.

In many states, shoppers are required to pay unpaid sales taxes when they file state tax returns. But governors complain that few people comply.

Under the bill, states that want to collect online sales taxes must provide free computer software to help retailers calculate the taxes, based on where shoppers live. States must also establish a single entity to receive Internet sales tax revenue, so retailers don’t have to send them to individual counties or cities.