OK, I finally figured this out. Here is what I did.
DbFunctionCall getDate = new DbFunctionCall("GETDATE", new object[] { });
DbFunctionCall dateAddStart = new DbFunctionCall("DATEADD(DAY, 14, {0})", new object[] { NominationFields.ActivatedDate });
DbFunctionCall dateAddEnd = new DbFunctionCall("DATEADD(DAY, 28, {0})", new object[] { NominationFields.ActivatedDate });
IPredicate startDayFilter = (NominationFields.ActivatedDate.SetExpression(getDate) >= dateAddStart);
IPredicate endDayFilter = (NominationFields.ActivatedDate.SetExpression(getDate) <= dateAddEnd);
PredicateExpression dayFilter = new PredicateExpression();
dayFilter.AddWithAnd(startDayFilter);
dayFilter.AddWithAnd(endDayFilter);
filter.PredicateExpression.AddWithAnd(dayFilter);