“As far as the absolute dollars go it’s woefully, woefully short,” said Gary Mendell, the founder and chief executive of Shatterproof, an anti-addiction advocacy group. “What you need is funding flowing into the health care system, so that patients are treated by primary care doctors, by behavioral therapists, get medication-assisted treatment.”

The current version of the Senate bill provides only $2 billion “to support substance use disorder treatment and recovery support services for individuals with mental or substance use disorders,” and only in the 2018 fiscal year. Adding more money for addiction treatment is aimed at winning crucial votes from a handful of moderate Republicans whose states have been particularly hard hit by the opioid crisis. Foremost among them are the Republican Senators Rob Portman of Ohio and Shelley Moore Capito of West Virginia, whose states have some of the nation’s highest overdose death rates.

But Ms. Capito and Mr. Portman, who have also expressed concern about the bill’s substantial reductions in overall Medicaid funding, have suggested they would not be swayed by the promise of extra opioid money alone.

Senator Maggie Hassan, a Democrat of New Hampshire, another opioid-ravaged state, dismissed $45 billion as “a drop in the bucket that would not come close to making up for the damage” that would be inflicted by the broader cuts to federal Medicaid spending in the bill, which the Congressional Budget Office estimated would amount to $772 billion by 2026.

Bertha K. Madras, a Harvard Medical School professor whom President Trump appointed to his new commission on the opioid crisis, said it was difficult to calculate how much would be needed to combat the epidemic. But she laid out a number of spending priorities that go beyond just treatment, including prevention efforts, support for children and families of the addicted and better analytics to figure out what is working and what is not. Like other experts, she emphasized the importance of combining addiction treatment with broader medical care.

In the short term, the grants suggested in the Senate plan would be most helpful in the 19 states that opted not to expand Medicaid under the Affordable Care Act. In those states, many poor people addicted to opioids still have little or no access to treatment. Additional federal grants for treatment would be better than nothing at all. In the 31 states that expanded Medicaid, the extra federal funding that paid for almost all of it would not begin phasing out until 2021.