BUFFALO, N.Y. — Targeting the soaring cost of higher education, President Barack Obama on Thursday unveiled a broad new government rating system for colleges that would judge schools on their affordability and perhaps be used to allocate federal financial aid.

But the proposed overhaul faced immediate skepticism from college leaders who worry the rankings could cost their institutions millions of dollars, as well as from congressional Republicans wary of deepening the government’s role in higher education.

The president, speaking to a student-heavy crowd of 7,000 at the University at Buffalo, said he expected pushback from those who have profited from the ballooning cost of college. But he argued that with the nation’s economy still shaky and students facing increasing global competition, making college affordable is “an economic imperative.”

The new rating system does not require congressional approval, and the White House is aiming to have it set up before the 2015 school year. But Obama does need support from Congress to use the ratings as a basis for parceling out federal financial aid.

In addition to tuition, schools will also be rated on average student loan debt, graduation rates and the average earnings of graduates. Under Obama’s proposal, students attending highly rated schools could receive larger grants and more affordable loans.

The president is also seeking legislation to give colleges a “bonus” based on the number of students they graduate who received Pell Grants. The goal is to encourage colleges to enroll and graduate low- and moderate-income students.

Obama’s other proposals include a requirement that colleges with high dropout rates distribute student aid over the course of the semester rather than in a lump sum. The aim is to ensure that students who drop out do not receive funds for time they are not in school.

However, if colleges line up against the idea of tying ratings to federal aid, the proposal would face nearly impossible odds.

Almost all members of Congress have colleges or universities in their districts, and a coordinated effort to rally students and educators against the plan would probably kill it quickly.