Sen. James H. Webb Jr., a Virginia Democrat, has secured 58 co-sponsors for his legislative effort to expand education benefits for veterans of Iraq and Afghanistan, only two votes shy of the 60 needed to overcome a filibuster. But there’s one crucial sponsor he hasn’t been able to get: fellow Vietnam veteran John McCain.

Mr. McCain, the presumptive Republican nominee, has come under intense pressure from veterans groups to endorse Mr. Webb’s bill, which would cover up to the full cost of a four-year education at a public college. Supporters see Mr. McCain’s backing as key to the bill’s prospects.

But the senator, who often touts his military credentials on the campaign trail, has so far refused to sign on, and last week said he will co-sponsor a less costly Republican alternative. That bill, which has far fewer co-sponsors than Mr. Webb’s bill, would provide a smaller initial benefit but raise the award after 12 years of service to encourage re-enlistment. The Defense Department has warned that providing too generous an educational benefit could harm retention rates.

In an interview with the Capitol Hill publication Politico Mr. McCain said that “there are fundamental differences” between Mr. Webb’s bill and the proposed alternative.

“He creates a new bureaucracy and new rules,” he said. “His bill offers the same benefits whether you stay three years or longer. We want to have a sliding scale to increase retention.”

But supporters of Senator Webb’s measure aren’t giving up. Their bill is likely to be attached to a war spending measure that Congress is expected to take up soon, and Mr. Webb is closing in on the crucial 60 votes.