The Obama administration is trying to push through a settlement over mortgage-servicing breakdowns that could force America’s largest banks to pay for reductions in loan principal worth billions of dollars. Terms of the administration’s proposal include a commitment from mortgage servicers to reduce the loan balances of troubled borrowers who owe more than their homes are worth, people familiar with the matter said. The cost of those writedowns won’t be borne by investors who purchased mortgage-backed securities, these people said.