Final answer:
The assertion that state constitutions grant the cabinet the power to amend the governor's proposed budget and to review line-item vetoes is false. Governors possess the power to veto and have significant influence over budget proposals, although the Legislature may override vetoes.
Step-by-step explanation:
The statement that the state constitution gives the cabinet a number of policy-making responsibilities, including amending the governor's proposed budget and reviewing all line-item vetoes, is generally false. In most states, the governor has the power to veto any bill passed by the Legislature, including the authority to exercise a line-item veto, which allows the governor to strike out individual portions of budget bills. However, any veto can be overridden by the Legislature, usually by a two-thirds vote.
The governor also has the responsibility of initiating a budget proposal, which sets funding priorities and indicates the amounts to be appropriated to different state agencies. While the Legislature can modify this proposal, the governor often has a strong influence on the final budget due to their veto and budget-setting powers.
It's also important to note the role of the governor in influencing the legislative process, through not only vetoes but also their policy agenda and executive budget proposals. This influence can impact how funds are allocated and which initiatives are prioritized by the state government.