Democrats overwhelmingly helped the legislation get over a procedural hurdle Monday evening, however. They have been tight-lipped on whether they would be willing to sink the Comprehensive Addiction and Recovery Act (CARA).
Durbin, however, suggested that he didn't know what his Republican counterpart was talking about.
"I'd like to ask my friend from Texas to show me the money," Durbin told reporters.
Whitehouse appeared to back Durbin's comments on the Senate floor while suggesting that lawmakers need to do some soul searching and talk with constituents about the "right way to vote" on the Democratic push for funding.
"I will fight as hard as I can to make sure that this bill is adequately funded, but I do not intend nor do I know anyone who intends to block the passage of CARA or to interfere with it going into law over the question of funding," he said.
CARA authorizes — but doesn't appropriate — funding for programs to combat prescription drug and heroin abuse, in addition to increasing the availability of naloxone, a drug to treat overdoses.
Democrats argue that the the emergency funding is needed to make sure communities who are fighting the overdose epidemic can get help quickly.
It would also be an election-year boon for Portman, who faces a tough reelection bid and has put the drug crisis at the forefront of his campaign.
Durbin, however, warned that voters would see through a "stunt" if Republicans support the Portman-Whitehouse bill but don't agree to include the funding pushed for by Democrats.
"I think ultimately the public will see through it, if the Republicans won't pay for it and won't come up with the resources," he said. "Republicans who vote against paying for it ... have something to explain back home."
—Updated at 6:02 p.m.