Creating a Stored Procedure that will input data for each day between the date entered as input to or from the 1st of that month
I reduced your statement down to the simplest possible piece of code, and found the exact error.  I removed everything except the loop, and got to this:

CREATE PROCEDURE dbo.test
(
    @ProductionDate As DateTime
    , @Debug BIT = 1
)
AS
BEGIN
    SET NOCOUNT ON;

    DECLARE @BegMonth As DateTime

    SET @BegMonth = DATEADD(MONTH, DATEDIFF(MONTH, 0, GETDATE()), 0)

    WHILE @productionDate &gt;= @BegMonth
        SELECT @endDate = DATEADD(DAY, 1, @BegMonth)
END


The WHILE statement does not have BEGIN directly afterwards.  This means the WHILE loop is essentially this:

WHILE @productionDate &gt;= @BegMonth SELECT @endDate = DATEADD(DAY, 1, @BegMonth)


and nothing else.  Just, loop forever.

To fix it, make your code like this:

USE [OperationsView]
GO
/****** Object:  StoredProcedure [Interface].[proc_GetChemicalDaily] Script    Date: 1/30/2017 4:03:51 PM ******/
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
-- =============================================
-- Author:      &lt;Author,,Name&gt;
-- Create date: &lt;Create Date,,&gt;
-- Description: &lt;Daily Chemical&gt;
-- =============================================
ALTER PROCEDURE [Interface].[proc_GetChemicalDaily]
-- Add the parameters for the stored procedure here

@ProductionDate As DateTime,
@Debug BIT = 1

AS
BEGIN
-- SET NOCOUNT ON added to prevent extra result sets from
-- interfering with SELECT statements.
SET NOCOUNT ON;

-- pi sproc variables Declaration
DECLARE @result As Float
DECLARE @tag_in As varchar(80)
DECLARE @pi_server As varchar(50)
DECLARE @enddate As DateTime
DECLARE @FCChemGALPERMIN float
DECLARE @CAUSTICDAILYUSAGE As Decimal(16, 8)
DECLARE @constant As Decimal(16, 8)
DECLARE @BegMonth As DateTime

--Actual variables for insertion
DECLARE @Group As VARCHAR(200)
DECLARE @Item As VARCHAR(200)
DECLARE @Total As DECIMAL(20, 4)
DECLARE @Days As Int
DECLARE @Type As VARCHAR(1)


--Pi Sproc variable setting
   SELECT @tag_in = 'I-FC-835'
   SELECT @pi_server = 'valpi'
   SET @constant = (18318.0/2000.0)*.5
   SET @BegMonth = DATEADD(MONTH, DATEDIFF(MONTH, 0, GETDATE()), 0)

   --Setting Actual insertion variables
   SET @Group = 'CHEMICAL'
   SET @Item = 'CAUSTIC CHEM'
   SET @Days = 1
   SET @Type ='a'
   --create temp table to grab decimal value
   create table #temp
   (
    float_col   float,
    percent_col float
   )
--Grabbing gal/min value from PI
While @productionDate &gt;= @BegMonth
BEGIN
     SELECT @endDate = DATEADD(DAY, 1, @BegMonth)
     INSERT into #temp(float_col, percent_col)
     EXEC Interface.proc_GetPIValueAverageTime @result, @tag_in, @BegMonth, @endDate, @pi_server, @Debug 
     SELECT @FCChemGALPERMIN = float_col FROM #temp

  -- daily dry ton usage calculation
  IF @FCChemGALPERMIN &gt; .5
 SET @CAUSTICDAILYUSAGE = cast(@FCChemGALPERMIN*@constant as numeric(38,10))
  ELSE
 SET @CAUSTICDAILYUSAGE = 0.0000

--Inserting in Actuals table
IF @Debug = 1

begin
    INSERT INTO [OperationsView].[dbo].[Actuals]
            ([Group]
            ,[Item]
            ,[ProductionDate]
            ,[Days]
            ,[Total]
            ,[Type])
        VALUES
            (@Group
            ,@Item
            ,@ProductionDate
            ,@Days
            ,@CAUSTICDAILYUSAGE
            ,@Type);                    
end 

DROP TABLE #temp
Set @BegMonth = DATEADD(DAY, 1, @BegMonth)
 END
END