Signers include food, beverage and supermarket companies; public health, education, anti-hunger, faith-based, children's, women's, minority groups; and unions. They want the House to pass a $4.5 billion bill that cleared the Senate by unanimous consent just before the August recess.

The groups are increasingly defending the reauthorization as a key tool to fight childhood obesity — the goal of Obama's Let's Move campaign. The First Lady, meanwhile, spent Veterans Day Thursday helping to feed U.S. servicemembers and their families at the Ramstein Air Base in Ramstein, Germany.

The Senate version of the child nutrition bill, championed by Sen. Blanche Lincoln (D-Ark.), expands eligibility for school meal programs; establishes nutrition standards for all foods sold in schools; and provides a 6-cent increase for each school lunch to help cafeterias serve healthier meals. Despite the bill's bipartisan appeal, passage in the House has been stymied by liberal Democrats and some anti-poverty advocates who are balking at paying for half the bill ($2.2 billion) by ending a temporary increase in food stamp payments five months early, in November 2013.

The letter signers say they share that concern but are confident that a solution to the food-stamp cuts can be found after the bill is passed "through other timely legislative or administrative vehicles."

"In urging a compromise that addresses our concerns through separate vehicles," reads the letter, "we seek to move beyond the impasse holding up passage of the bill and the improved nutrition our children need."

Separately, a group of about 20 food and agricultural suppliers also wrote this week to Miller and Kline to support passage of the Senate bill.

"We join the many other public health and nutrition groups who have come together to support passage and enactment of S. 3307 now," their letter states, "and we stand ready to help you achieve that goal."