Adjective to describe the intentionally slow U.S. legislative process

Perhaps deliberate:

adj.

1. carefully weighed or considered; studied; intentional.
2. characterized by deliberation or cautious consideration; careful or slow in deciding.
3. leisurely and steady in movement or action; slow and even; unhurried: moving with a deliberate step.

There's also the overused (in my opinion) Kafkaesque. It's close, although not exactly what you're after, since it usually implies a frustrating, perhaps unnecessary complexity as well, rather than an intentional well-behaved slowness:

adj.

2. marked by a senseless, disorienting, often menacing complexity.

I would go with deliberate, or a related word like careful, cautious, painstaking, etc.

There is also gradual, I suppose, although it feels strange to me here for reasons that I can't explain. You may have some success with it or one of its synonyms, though:

adj.

1. taking place, changing, moving, etc., by small degrees or little by little.

^{(All definitions from Dictionary.com)}

Throttled (adj.) or throttling, from the verb throttle. — M-W

verb 3. to not allow (something) to grow or develop

Throttle — Wiktionary

verb (transitive) 1. To cut back on the speed of (an engine, person, organization, network connection, etc.).

Example usages:

1. Throttled data transfer — TechTarget

   Data transfer throttling is often used to prevent spam or bulk e-mail transmission through a network server. If the number of e-mail messages sent through the server is limited to, say, one destination address per minute, it is impossible for that server to effectively operate as a medium for the transmission of spam because it would take weeks or months to transfer the number of messages necessary for effective spam marketing

2. Bandwidth throttling — Wikipedia

   Bandwidth throttling is the intentional slowing of Internet service by an Internet service provider. It is a reactive measure employed in communication networks to regulate network traffic and minimize bandwidth congestion.

3. Throttling process (computing) — Wikipedia

   In software, a throttling process, or a throttling controller as it is sometimes called, is a process responsible for regulating the rate at which application processing is conducted, either statically or dynamically.

Consider bureaucratic. This word tends to carry connotations of intentional or even excessive slowness.

[...]

3. excessive multiplication of, and concentration of power in, administrative bureaus or administrators.

4. administration characterized by excessive red tape and routine.

I would think that 'glacial', with the addition of 'pace' at the end, sums it up nicely.

glacial adj. Extremely slow, like the movement of a glacier: Work proceeded at a glacial pace.

Source: The Free Dictionary

glacial pace 'At a glacial pace' means 'very slowly'.

Source: Urban Dictionary

I would go with conservative. If memory serves, I've read in political science textbooks and political commentary the American political system described as conservative, and not in the sense of a political ideology.

Dictionary.com

having the power or tendency to conserve or preserve.

Merriam-Webster.com

tending or disposed to maintain existing views, conditions, or institutions

But I would caution that use of this word might lead careless readers to think you were stating that the American political system was inherently conservative as a political philosophy. If you do decide to use this word I would explain that.