Thanks for setting me in the right direction...
CREATE TABLE #Holidays (HolidayDate datetime, IsHoliday char(1))
INSERT INTO #Holidays (HolidayDate,IsHoliday) VALUES('2013-02-18 00:00:00.000', 'Y')
INSERT INTO #Holidays (HolidayDate,IsHoliday) VALUES('2013-03-29 00:00:00.000', 'Y');
DECLARE @StartDate DATETIME
SET @StartDate = '2/15/2013'
SELECT
MIN((DATEADD(dd, DATEDIFF(dd, 0, @StartDate), 0) + n))
FROM TALLY T
LEFT JOIN #Holidays H
ON HolidayDate = (DATEADD(dd, DATEDIFF(dd, 0, @StartDate), 0) + n)
WHERE
HolidayDate IS NULL AND
DATEPART(WEEKDAY, (DATEADD(dd, DATEDIFF(dd, 0, @StartDate), 0) + n)) NOT IN (7,1)
DROP TABLE #Holidays