I had another suggestion (from a different forum) that provided a solution. It may not be the most eloquent but it ran on 98K rows in 8 minutes.

This is from "Lamprey" on the SQLTeam .com forum:

DECLARE @Foo TABLE (ITEM1 INT, ITEM2 INT, ID INT)

INSERT @Foo (ITEM1, ITEM2) VALUES

(0224180, 0224181),

(0224180, 0224190),

(0224181, 0224180),

(0224181, 0224190),

(0224190, 0224180),

(0224190, 0224181),

(0202294, 0202295),

(0202295, 0202294),

(0209250, 0209251),

(0209251, 0209250)

DECLARE @Val1 INT;

DECLARE @Val2 INT;

DECLARE @Iterator INT = 1;

-- Prime Loop

SELECT TOP 1

@Val1 = Item1,

@Val2 = Item2

FROM

@Foo

ORDER BY

Item1

WHILE @Val1 IS NOT NULL

BEGIN

-- Perform Update

UPDATE

@Foo

SET

ID = @Iterator

WHERE

Item1 IN (@Val1, @Val2)

OR Item2 IN (@Val1, @Val2);

-- Get next item/group

SELECT TOP 1

@Val1 = Item1,

@Val2 = Item2

FROM

@Foo

WHERE

Item1 NOT IN (@Val1, @Val2)

AND Item2 NOT IN (@Val1, @Val2)

AND ID IS NULL

ORDER BY

Item1

IF @@ROWCOUNT = 0

BEGIN

SET @Val1 = NULL;

END

SET @Iterator = @Iterator + 1;

END

SELECT *

FROM @Foo