Updated

The case of Shakil Afridi, the Pakistani doctor imprisoned after helping the CIA track Usama bin Laden, hasn't fallen by the wayside just yet.

Sen. Rand Paul claims to have enough support to force a vote on the Senate floor later this month on a bill stripping Pakistan of U.S. aid unless Afridi is released.

The vote, if it happens, would come at a diplomatically inconvenient time for the Obama administration. The State Department recently announced it had struck a deal with Pakistan to reopen long-shuttered supply lines into Afghanistan -- the thaw came after Secretary of State Hillary Clinton publicly apologized for a NATO strike last fall that killed 24 Pakistani soldiers.

Following the agreement, top Capitol Hill lawmakers signaled they would free up $1.1 billion in U.S. aid to Pakistan that had been held up for six months over the standoff.

But Paul, R-Ky., wants to push ahead on his vote anyway, citing Afridi's plight. The bill apparently could not stop the $1.1 billion from being transferred, but aims to lock down future funds.

Paul appears to be giving Pakistan one more chance before moving ahead. Paul spokeswoman Moira Bagley told FoxNews.com the senator is eyeing July 20 for a vote, one day after a scheduled July 19 appeal date for Afridi. Bagley described the July 20 vote as "tentative ... pending results of Dr. Afridi's appeal."

Though congressional leaders reportedly are opposed to the vote, Bagley said Paul has enough signatures on what's known as a cloture petition to force one anyway.

Afridi's cause has over the past several weeks become somewhat buried amid the far-louder debates over health care, taxes, immigration and the presidential campaign itself.

On the House side, Rep. Dana Rohrabacher, R-Calif., has been pressing Afridi's case for weeks, ever since the Pakistani doctor was sentenced in May to 33 years in prison. But Rohrabacher recently expressed concern that lawmakers and other officials were losing interest in the case.

"It doesn't appear that other people are taking this case seriously," Rohrabacher told FoxNews.com last month. "If we let that person just hang on a limb and forget him, now that he's put himself in danger for us -- well shame on us."

But Paul has been quietly pressing Afridi's case from the upper chamber. According to Bagley, Paul spoke with Pakistani Ambassador to the U.S. Sherry Rehman, as well as the top representative to the region from the State Department. She said he remains hopeful Pakistan will free Afridi.

Afridi's brother Jamil told Fox News in May that Shakil Afridi had suffered torture while in custody ahead of his sentencing. At the time, Jamil Afridi appealed for the U.S. Embassy to help fight his legal case.

The State Department has said it's still focused on the case, and that it continues to urge Pakistan to consider his appeal in an "expeditious" and "transparent" manner.

Without addressing the Afridi case, State Department spokesman Patrick Ventrell said last week after the border-crossing agreement that "we're really looking to moving forward with Pakistan in our relationship as best we can."

Meanwhile, lawmakers are moving ahead with plans to free up the $1.1 billion in Pakistan aid sidelined since last fall.

Senate Armed Services Committee Chairman Carl Levin, D-Mich., and one of the panel's top Republicans, Lindsey Graham, said the money should be released, albeit reluctantly.

"They don't deserve it. What they've done is presumably earned it by the amount of money they've laid out in terms of their anti-terrorist activity and protecting our lines," Levin told a group of reporters earlier this week.

He said he would vote to approve the release.

The Pentagon intends to submit $1.1 billion in approved requests for reimbursement of money the Pakistan government has spent on counterterrorism operations that were incurred largely along the border.

"If you cut the money off, what leverage do you have? There may come a day when we do that, but not yet," Graham said.

FoxNews.com's Judson Berger and The Associated Press contributed to this report.