It's the US Constitution that stipulates that each State has control over how voting is conducted within that State. The HAVA act only passes as 'constitutional' in that the Federal government is attempting to 'strong arm' the states into dumping their chosen voting systems in order to get Federal funds. Note that the HAVA Act does not 'outlaw' the use of those technologies directly, (Punch Cards and Lever Machines) it only outlaws a state from receiving HAVA funds if they continue to use those technologies.
Text of the HAVA Act<snip>
SEC. 102. <<NOTE: 42 USC 15302.>> REPLACEMENT OF PUNCH CARD OR LEVER
VOTING MACHINES.
(a) Establishment of Program.--
(1) In <<NOTE: Deadline.>> general.--Not later than 45 days
after the date of the enactment of this Act, the Administrator
shall establish a program under which the Administrator shall
make a payment to each State eligible under subsection (b) in
which a precinct within that State used a punch card voting
system or a lever voting system to administer the regularly
scheduled general election for Federal office held in November
2000 (in this section referred to as a ``qualifying precinct'').
(2) Use of funds.--A State shall use the funds provided
under a payment under this section (either directly or as
reimbursement, including as reimbursement for costs incurred on
or after January 1, 2001, under multiyear contracts) to replace
punch card voting systems or lever voting systems (as the case
may be) in qualifying precincts within that State with a voting
system (by purchase, lease, or such other arrangement as may be
appropriate) that--
(A) does not use punch cards or levers;
(B) is not inconsistent with the requirements of the
laws described in section 906; and
(C) meets the requirements of section 301.
(3) Deadline.--
(A) In general.--Except as provided in subparagraph
(B), a State receiving a payment under the program under
this section shall ensure that all of the punch card
voting systems or lever voting systems in the qualifying
precincts
<[Page 116 STAT. 1671>]
within that State have been replaced in time for the
regularly scheduled general election for Federal office
to be held in November 2004.
(B) Waiver.--If a State certifies to the
Administrator not later than January 1, 2004, that the
State will not meet the deadline described in
subparagraph (A) for good cause and includes in the
certification the reasons for the failure to meet such
deadline, the State shall ensure that all of the punch
card voting systems or lever voting systems in the
qualifying precincts within that State will be replaced
in time for the first election for Federal office held
after January 1, 2006.