WASHINGTON -- Senator Claire McCaskill, one of several lawmakers leading a new effort to combat sexual assault on colleges campuses, said Monday that she’s eyeing stiffer penalties for institutions that violate federal rules on reporting and handling sexual assault cases.

Kicking off the first of three Capitol Hill roundtable discussions on the issue, McCaskill previewed some of the issues she plans to tackle in legislation she is drafting with Senators Kirsten Gillibrand of New York and Richard Blumenthal of Connecticut.

The bill, she said, would aim to simplify the “complex labyrinth” of rules that govern campus sexual assaults: the Clery Act, the federal antidiscrimination law known as Title IX, and a patchwork of state laws that define consent.

But McCaskill also indicated that the lawmakers are seeking to take a harder line against colleges that violate those rules. The lawmakers, she said, are considering a revised penalty structure for the Clery Act and Title IX.

She said that the complete removal of federal funds -- the most severe sanction federal officials can currently impose on institutions -- is unrealistic for the government to impose without unfairly harming large numbers of innocent students. But at the other extreme, the maximum $35,000 fine that can be levied under the Clery Act is essentially a slap on the wrist for many institutions.

“We’re looking at a variety of things, including larger fines,” she said. “I feel very strongly that fines would need to be based on the size of the institution.”

She said she was still considering whether an institution’s size should be measured by its budget, its enrollment, or the degree to which it receives federal aid.

McCaskill said she also wanted to codify in the legislation a requirement that colleges use the “preponderance of the evidence” standard in adjudicating sexual assault cases on campus. The Obama administration has told colleges that it believes such a standard is required by Title IX, but McCaskill said that it should be written into law.

Another part of the legislative effort, McCaskill said, will be focused on ways to incentivize states to change their rules regarding consent. She said she was disappointed to learn that 16 states do not recognize a person’s incapacitation as a reason why he or she cannot provide consent.

In addition, the legislation will include a requirement that colleges conduct anonymous surveys on their campus to learn about the “climate” surrounding sexual assault and harassment on their campus. The White House has asked colleges to consider using such surveys this year and also floated the notion of making them mandatory.

McCaskill, who has already sparred with the main higher education lobbying association over how it was counseling members to respond to a survey she sent to colleges about sexual assault, said Monday that she had received some pushback from colleges over making climate surveys mandatory.

“We’re going to look at the annual cost of doing an annual climate survey, but I think that with this problem and with the attention that it is finally receiving, I think many universities are going to be reluctant to shirk away from the responsibility of finding out the actual extent of the problem they have on their campus.”

Monday’s roundtable was focused specifically on the Clery Act, which requires colleges to report the crimes that happen on their campus, including sexual assault, rape and dating violence.

Participants told McCaskill and Senator Tammy Baldwin of Wisconsin that many of the current reporting requirements are confusing or solicit information that is not complete or useful to students who want to know the relative safety of a given campus.

Several of the university-affiliated panelists called for the government to publish model policies and best practices for institutions. Others said the federal government should step up its oversight of how colleges are handling sexual assault cases, a concern that McCaskill echoed.

Laura Dunn, executive director of SurvJustice, told the panel that “if you’re going to spend money somewhere, please spend it on enforcement.”

Lynn Mahaffie, who directs policy in the Education Department’s Office of Postsecondary Education, said the agency has assigned 13 people to a special Clery Act compliance unit, which completes about 20 audits under that law each year. Departmentwide, there are about 300 such cases each year, she said.

McCaskill said that level of staffing seemed too low to handle thousands of colleges.