The way I read it is that every time a new Congress convenes, they adopt a set of procedures and rules to operate buy. The House uses Jefferson's Rules, so it is not tradition, but something that they vote on in a binding manner every two years.
And in that binding manner, if a state legislature does send it to the House, by Jefferson's Rules all House business ceases until the issue is resolved. It is 'privileged' of the highest order.
<snip>
In the <<NOTE: Sec. 603. Inception of impeachment proceedings in the
House.>> House there are various methods of setting an impeachment in
motion: by charges made on the floor on the responsibility of a Member
or Delegate (II, 1303; III, 2342, 2400, 2469; VI, 525, 526, 528, 535,
536); by charges preferred by a memorial, which is usually referred to a
committee for examination (III, 2364, 2491, 2494, 2496, 2499, 2515; VI,
543); by a resolution dropped in the hopper by a Member and referred to
a committee (Apr. 15, 1970, p. 11941; Oct. 23, 1973, p. 34873); by a
message from the President (III, 2294, 2319; VI, 498); by charges
transmitted from the legislature of a State (III, 2469) or territory
(III, 2487) or from a grand jury (III, 2488); or from facts developed
and reported
<<Page 315>>
by an investigating committee of the House (III, 2399, 2444).
<snip>
A direct <<NOTE: Sec. 604. A proposition to impeach a question of
privilege.>> proposition to impeach is a question of high privilege in
the House and at once supersedes business otherwise in order under the
rules governing the order of business (III, 2045-2048, 2051, 2398; VI,
468, 469; July 22, 1986, p. 17294; Aug. 3, 1988, p. 20206; May 10, 1989,
p. 8814; Sept. 23, 1998, pp. 21560-62; see Deschler, ch. 14, Sec. 8). It
may not even be superseded by an election case, which is also a matter
of high privilege (III, 2581). It does not lose its privilege from the
fact that a similar proposition has been made at a previous time during
the same session of Congress (III, 2408), previous action of the House
not affecting it (III, 2053). As such, a report of the Committee on the
Judiciary accompanying an impeachment resolution is filed from the floor
as privileged (Dec. 17, 1998, p. 27819), and is called up as privileged
(Dec. 18, 1998, p. 27828). The addition of new articles of impeachment
offered by the managers but not reported by committee are also
privileged (III, 2401), as is a proposition to refer to committee the
papers and testimony in an impeachment of the preceding Congress (V,
7261).
<snip>
http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=109_cong_house_rules_manual&docid=hruletx-57http://www.gpoaccess.gov/hrm/browse_109.htmlThis has never been done before, so if it does happen it should be quite... interesting! :-)