He ran for governor again in 1852 under the new constitution—with an extended four year gubernatorial term—defeating against Whig Nicholas McCarty, and Free Soiler John Cravens.
Wright won again with 95,576 votes to McCarty's 73,641, and Craven's 3,308.
There was a brief contention about the legality of his second term.
The new state constitution banned governors from serving consecutive terms, but it was decided that because his original term occurred under the old constitution, he was still eligible to serve.

In 1855, another bill was passed to permit the Bank of Indiana to incorporate privately, and was also vetoed by Wright.
The General Assembly again overrode his veto with a super-majority.
Before the passage of law that permitted the bank to reincorporate, Wright personally delivered a speech to the House of Representatives in which he harangued the bank and accused them of "corruption and fraud", and alluded that the bank had bribed members of the General Assembly to pass the bill.

Wrights speech put him at odds with the Democrat-controlled legislature and severely hurt his relationship with them, including the lieutenant governor, who was a major supporter of the bill.
Unhappy with the outcome of the situation, Wright decided to continue in his attempt to prevent the new bank from operating and launched lawsuits against the bill and the bank in the state courts.
He demanded that the courts declare the law "null and void", but the circuit courts ruled against him.
He appealed to the Indiana Supreme Court, who ultimately ruled in favor of the bank.
With his legal options exhausted, Wright took the fight back to the legislature in 1857, giving a scathing speech accusing the body of many different violations of public good-will.
He went on to say that "the means and applications brought to bear to secure passage of charter, would if exposed, exhibit the nakedest exposition of fraud and corruption that ever disgraced the Legislature of this state".
The Senate responded by creating a commission to look into the accusations made by the Governor.
Although only a few minor infractions were found, the committee agreed that the circumstances surrounding the passage of the bill were questionable and recommended the bank's charter be revoked, but no action was taken.

In 1854, the first cracks in the state Democratic Party began to show after the passage of the Kansas-Nebraska Act by Congress.
Bright and his faction, a majority of the party, began forcing out anti-slavery members of the party leadership, using support of the act as a litmus test of party loyalty.
By then the national debate over the possible break-up of the Union had begun.
The Whig party was also on the brink of collapse, and a new coalition party of former Whigs, former Democrats, the anti-immigration Free Soil party, and the anti-slavery Liberty Party came together.
The result was the so-called Know-Nothing Party and the first real challenge to Democratic control of the state in a generation.
The 1854 mid-term election caused the Democrats to lose seats in the Senate, but still maintain control.
The Democrats did, however, lose their majority in the house.
The House was split with no party attaining majority, and the Whigs caucused with the Democrats to control the assembly.
The effect was a virtual paralysis to the legislature, and Wright was unable to make any significant accomplishments during his last two years in office.

The Washington Monument was under construction during Wright's term.
A strong supporter of the Union, Wright had a block sent for the monument with the inscription, "Indiana knows no East, no West, no North, no South; nothing but Union".
The stone eventually found its way into the monument where it remains today.
Wright left office popular with the public, but at odds with the leadership of his party.
His position on banking had cost him much of their support, and he was especially denounced by Jesse D. Bright for his support of the Union over states-rights.
He ran for governor again in 1852 under the new constitution—with an extended four year gubernatorial term—defeating against Whig Nicholas McCarty, and Free Soiler John Cravens. Wright won again with 95,576 votes to McCarty's 73,641, and Craven's 3,308. There was a brief contention about the legality of his second term. The new state constitution banned governors from serving consecutive terms, but it was decided that because his original term occurred under the old constitution, he was still eligible to serve.
In 1855, another bill was passed to permit the Bank of Indiana to incorporate privately, and was also vetoed by Wright. The General Assembly again overrode his veto with a super-majority. Before the passage of law that permitted the bank to reincorporate, Wright personally delivered a speech to the House of Representatives in which he harangued the bank and accused them of "corruption and fraud", and alluded that the bank had bribed members of the General Assembly to pass the bill.
Wrights speech put him at odds with the Democrat-controlled legislature and severely hurt his relationship with them, including the lieutenant governor, who was a major supporter of the bill. Unhappy with the outcome of the situation, Wright decided to continue in his attempt to prevent the new bank from operating and launched lawsuits against the bill and the bank in the state courts. He demanded that the courts declare the law "null and void", but the circuit courts ruled against him. He appealed to the Indiana Supreme Court, who ultimately ruled in favor of the bank. With his legal options exhausted, Wright took the fight back to the legislature in 1857, giving a scathing speech accusing the body of many different violations of public good-will. He went on to say that "the means and applications brought to bear to secure passage of charter, would if exposed, exhibit the nakedest exposition of fraud and corruption that ever disgraced the Legislature of this state". The Senate responded by creating a commission to look into the accusations made by the Governor. Although only a few minor infractions were found, the committee agreed that the circumstances surrounding the passage of the bill were questionable and recommended the bank's charter be revoked, but no action was taken.
In 1854, the first cracks in the state Democratic Party began to show after the passage of the Kansas-Nebraska Act by Congress. Bright and his faction, a majority of the party, began forcing out anti-slavery members of the party leadership, using support of the act as a litmus test of party loyalty. By then the national debate over the possible break-up of the Union had begun. The Whig party was also on the brink of collapse, and a new coalition party of former Whigs, former Democrats, the anti-immigration Free Soil party, and the anti-slavery Liberty Party came together. The result was the so-called Know-Nothing Party and the first real challenge to Democratic control of the state in a generation. The 1854 mid-term election caused the Democrats to lose seats in the Senate, but still maintain control. The Democrats did, however, lose their majority in the house. The House was split with no party attaining majority, and the Whigs caucused with the Democrats to control the assembly. The effect was a virtual paralysis to the legislature, and Wright was unable to make any significant accomplishments during his last two years in office.
The Washington Monument was under construction during Wright's term. A strong supporter of the Union, Wright had a block sent for the monument with the inscription, "Indiana knows no East, no West, no North, no South; nothing but Union". The stone eventually found its way into the monument where it remains today. Wright left office popular with the public, but at odds with the leadership of his party. His position on banking had cost him much of their support, and he was especially denounced by Jesse D. Bright for his support of the Union over states-rights.
Joseph A. Wright