Rother also said having the ACP join the campaign would help "bring pressure" to change the current pricing situation.
The campaign said that specialty prescription medicine prices are "skyrocketing," noting that in 2013 "specialty drugs accounted for less than 1 percent of U.S. prescriptions but for more than 25 percent of prescription spending." The campaign noted predictions by CVS Health that specialty drugs, by the end of the decade, "will account for roughly 50 percent of the total drug spend" despite being just 2 to 3 percent of all prescriptions.
"There appears to be no end in sight ... to the price increase. And even more troubling is there appears to be no justification for the prices drug companies are charging," Rother said. "Simply put, the prices for these drugs are unsustainable, and every day patients and their doctors are confronting this reality."
Concern about rising costs of specialty drugs has been gaining increased attention since the 2013 launch of Sovaldi, a highly successful hepatitis C medication manufactured by Gilead that costs an eye-popping $84,000 for a 12-week regimen. Hepatitis C, which is a liver disease, affects more than 3 million Americans.
Read MoreThe $84,000 question: Will focusing on drug prices rein in costs?
Drug manufacturers argue that they are entitled to recoup the sky-high costs of developing new treatments as well as to make a profit. But the high prices are counteracting a historic slowdown in health-care spending growth, and putting stress on government-run Medicaid and Medicare programs, which cover the poor and elderly, respectively. Those programs are the largest purchasers of health services in the U.S.
A Robert Wood Johnson Foundation report issued last week found that "most" of the 4.7 percent growth in health-care spending in the first half of 2014, compared to 3.6 percent in the same period of 2013, "was attributable to a jump in spending on prescription drugs—specialty drugs in particular."
"As for the fourth quarter [of 2014] spending on prescription drugs continued its rapid growth, on average 11 percent higher for October and November as compared to the same months last year," wrote Katherine Hempstead, the author of that report.
On the same day as that report, data released as part of the Truveris National Drug Index found that the prices of brand-name drugs increased by nearly 15 percent in 2014, while the prices of specialty drugs "jumped 9.7 percent." After factoring in a 4.9 percent increase in the price of generic drugs, Americans were paying, on average, 10.9 percent more for prescription medication last year compared to 2013.
Read MoreHHS wants power to negotiate specialty drug prices
"Drug costs across all categories are becoming an escalating concern for patients, employers, insurers and lawmakers," said Bryan Birch, chairman, president and CEO of Truveris, which analyzes drug pricing and benefits. "Looking at macro-industry trends, including consolidation, regulation and formulary pressure, we expect this price inflation to continue to put pressure on American households and employers in 2015."