After Senator Tom Coburn, Republican of Oklahoma, this month proposed prohibiting the National Science Foundation from “wasting any federal research funding on political science projects,” political scientists rallied in opposition, pointing out that one of this year’s Nobel winners had been a frequent recipient of the very program now under attack.

Yet even some of the most vehement critics of the Coburn proposal acknowledge that political scientists themselves vigorously debate the field’s direction, what sort of questions it pursues, even how useful the research is.

Much of the political science work financed by the National Science Foundation is both rigorous and valuable, said Jeffrey C. Isaac, a professor at Indiana University in Bloomington, where one new winner of the Nobel in economic science, the political scientist Elinor Ostrom, teaches. “But we’re kidding ourselves if we think this research typically has the obvious public benefit we claim for it,” he said. “We political scientists can and should do a better job of making the public relevance of our work clearer and of doing more relevant work.”

Mr. Isaac is the editor of Perspectives on Politics, a journal that was created by the field’s professional organization to bridge the divide after a group of political scientists led a revolt against the growing influence of statistical methods and mathematics-based models in the discipline. In 2000 an anonymous political scientist who called himself Mr. Perestroika roused scores of colleagues to protest the organization, the American Political Science Association, and its flagship journal, The American Political Science Review, arguing that the two were marginalizing scholars who focused on traditional research based on history, culture and archives.

Though there is still jockeying over jobs, power and prestige — particularly in an era of shrinking budgets — much of that animus has quieted, and most political scientists agree that a wide range of approaches makes sense.

What remains, though, is a nagging concern that the field is not producing work that matters. “The danger is that political science is moving in the direction of saying more and more about less and less,” said Joseph Nye, a professor at the John F. Kennedy School of Government at Harvard, whose work has been particularly influential among American policy makers. “There are parts of the academy which, in the effort to be scientific, feel we should stay away from policy,” Mr. Nye said, that “it interferes with the science.”

In his view statistical techniques too often determine what kind of research political scientists do, pushing them further into narrow specializations cut off from real-world concerns. The motivation to be precise, Mr. Nye warned, has overtaken the impulse to be relevant.

In recent years he and other scholars, including Robert Putnam and Theda Skocpol, both former presidents of the American Political Science Association, have urged colleagues not to shy away from “the big questions.”

Graduate students discussing their field, said Peter Katzenstein, a political science professor at Cornell University, often speak in terms of “an interesting puzzle,” a small intellectual conundrum that tests the ingenuity of the solver, rather than the large, sloppy and unmanageable problems that occur in real life.

“This is the great divide on what we are doing,” he said, adding that political scientists did not agree on the unit of analysis (whether the focus should be on the individual or social relationships), the source of knowledge or how to measure things.

Rogers Smith, a political scientist at the University of Pennsylvania who has been active in the “Perestroika” movement, said that the question should determine the method. If you want to test cause and effect, “quantitative methods are the preferred way to go,” he said, but they can’t tell “how political phenomena should be understood and interpreted” — whether a protest, for instance, is the result of a genuine social movement or an interest group, whether it is religious or secular.

Arthur Lupia, a professor in the University of Michigan’s political science department, said he was using the scientific method to understand what processes and institutions were necessary for a democratic society to function.

Mr. Lupia is the lead investigator on one of the projects financed by the National Science Foundation that Senator Coburn has attacked: the American National Election Studies. Senator Coburn has maintained that commentators on CNN, Fox News, MSNBC and other news media outlets “provide a myriad of viewpoints to answer the same questions.” He has argued that the $91.3 million that the foundation spent on social science projects over the last 10 years should have gone to biology, chemistry or pharmaceutical science.

Mr. Lupia, whose background is in applied mathematics and economics, concedes that political science is not quite like the natural sciences. First, the subjects under study “can argue back.” But he maintains that it uses the same rigorous mechanisms to evaluate observations as any other science.

The elections project, which has been financed by the foundation in various forms for more than three decades and has involved 700 scientists, tracks why citizens vote and how they respond to elections. The database is used by thousands of scholars, and has been widely praised as illuminating the question of why democracy works.

No date has been set for a vote on Senator Coburn’s proposal, which was introduced on Oct. 7. Yet even as he is trying to restrict National Science Foundation financing of social science, the Defense Department has been recruiting scholars in the same fields to work on security issues like terrorism, Iraq and China’s military. The nation must embrace “eggheads and ideas,” Defense Secretary Robert M. Gates has said, to meet potential national threats.

Some Defense Department grants were awarded by the Pentagon through a new program titled Minerva; others were distributed through the National Science Foundation because it has experience in grant making and is apolitical.

As for those who criticize quantitative analysis as too narrow, Mr. Lupia said that the big questions were precisely what interested him. His work has been used by the World Bank and government officials in India, for example, to figure out which villages had sufficient institutions and practices to ensure that money earmarked to build a water system would not end up in someone’s pocket. Political science can also help determine what institutions and arrangements are needed to help a dictatorship make the transition to a democracy, he added.

After the fall of Communism, “when Eastern European governments were writing their constitutions, I can guarantee you they weren’t calling George Stephanopoulos,” Mr. Lupia said.

“I try to identify problems and then identify solutions to them,” he said, “to find the type of scientific method” that can answer the question.