Washington (CNN) -- The House of Representatives approved $600 million in emergency funding Tuesday to help secure the U.S.-Mexico border.

The measure, which passed in a voice vote, still needs Senate approval before being signed into law by President Barack Obama.

Senators passed a similar plan last week, but must vote again on the House measure that includes the language on border funding. A top aide to Senate Majority Leader Harry Reid said Tuesday that the chamber could be recalled from its August recess to take up the House-approved measure.

"In light of the voice vote in the House, it is our hope that we can do this by consent by the end of the week," said Reid's spokesman, Jim Manley. "The question is whether Republicans want to try and make this an issue or whether they will allow us to get it done quickly."

Manley said Reid was waiting for word from Senate Republicans on whether they would object to approval by unanimous consent, which could be done without the return of the entire chamber.

Otherwise, Reid could still bring back the full Senate for a formal vote.

A Republican leadership source said Tuesday night that Republicans were likely to go along with passing the measure by unanimous consent.

Among other things, the bill provides for roughly 1,500 new law enforcement agents, new unmanned aerial vehicles, new forwarding operating bases and $14 million in new communications equipment.

The measure has attracted strong Democratic and Republican support. Homeland Security Secretary Janet Napolitano praised the plan last week, saying it would "add important, permanent resources to continue bolstering security on our Southwest border."

"These assets are critical to bringing additional capabilities to crack down on transnational criminal organizations and reduce the illicit trafficking of people, drugs, currency and weapons," she said.

The bill is funded in part by imposing higher fees on personnel companies that bring foreign workers into the United States.

CNN's Brianna Keilar contributed to this report