The Department of Veterans Affairs asked the public to write checks and donate food for homeless veterans.
The proposal is part of a massive $3 trillion coronavirus relief bill shaped by House Democrats.
The $300 million is over and above funds already being used.
The grants are available in high-cost areas, and also include job training.
Rankins said he hopes sharing his story at the State of the Union on Tuesday will make a difference for at least one veteran.
While veterans can live at the shelter for up to two years, their stay lasts about four to five months on average.
Not everyone has left the shelter on good terms. Eight veterans were unsuccessfully discharged from the shelter.
The plea comes in the case of a Good Samaritan story that raised more than $400,000 for homeless veteran Johnny Bobbitt Jr.
The veteran was likely on his way to a homeless encampment when he pedaled into the path of Terry Derilus' rental car.
HUD Secretary Ben Carson told reporters that the number of veterans who are homeless fell by 2% between 2018 and 2019.