Some states do, but I believe they have to either take their case in front of a judge after a reasonable length of time, have good reason, character witnesses, etc., or a state parole board.
Which brings me back to the punishment fitting the crime. Violent crimes should carry harsh penalties, That, and if they are repeat offenders, the punishment should increase with each violation.
But back to the OP, the Democrats probably will gain the votes of anyone given amnesty, because Democrats are overlooking the crime of them being here illegally.
In most states they simply have to complete their sentence before voting rights are restored:
In Maine and Vermont, felons never lose their right to vote, even while they are incarcerated.
In 14 states and the District of Columbia, felons lose their voting rights only while incarcerated, and receive automatic restoration upon release.
In 22 states, felons lose their voting rights during incarceration, and for a period of time after, typically while on parole and/or probation. Voting rights are automatically restored after this time period. Former felons may also have to pay any outstanding fines, fees or restitution before their rights are restored as well.
In 12 states felons lose their voting rights indefinitely for some crimes, or require a governor’s pardon in order for voting rights to be restored, or face an additional waiting period after completion of sentence (including parole and probation) before voting rights can be restored. These states are listed in the fourth category on Table 1. Details on these states are found in Table 2 below.
http://www.ncsl.org/research/elections-and-campaigns/felon-voting-rights.aspx