Under the proposed measure, Walker would not be allowed to order special elections this year. In January, a Democrat won a Wisconsin assembly seat in a heavily Republican district, an upset that Walker called a "wakeup call" for the GOP.
The Republican leaders of the state legislature also dropped plans to convene a special session to change Wisconsin law and cancel the elections.
After three separate judicial orders to call special elections to fill two vacant legislative seats, Gov. Scott Walker has complied with the rulings and issued an executive order to hold new elections.
The announcement came in a filing with the high court by the state Department of Justice, which represents Walker, late Wednesday that the governor would not ask the Supreme Court to overturn the appeals court.
"The Governor understands he has an obligation to follow the law as do we", wrote District 2 Court of Appeals Judge Paul F. Reilly.
The ruling by Circuit Judge Richard Niess doesn't affect proposed changes to the state law governing special elections that lawmakers are set to take up April 4.
The Wisconsin Elections Commission said Wednesday the last spring and fall elections cost $235,000 and $389,000 in Senate District 1 and cost $72,000 and $122,000 in Assembly District 42. But, this week, despite every effort by Scott Walker to avert the expression of the will of the people, democracy prevailed.
Wisconsin Democrats said Walker had refused to hold the elections because he was afraid Democrats might flip the seats. Miller said Republicans' proposal could leave residents of certain parts of the state without legislative representation. While some first responders are already treating pets at emergency scenes, they put themselves at professional risk while providing care as their actions are illegal under state law.
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A Madison judge last week ordered the Republican governor to schedule the elections by noon on Thursday.
Walker wanted Niess to extend the deadline in light of the Legislature's plans to pass a bill next week that would restrict special elections.
Florida Gov. Rick Scott, also a Republican, relied on a similar argument when he declined to call special elections last month.
Walker then asked another Dane County judge for a one week delay, in time for the legislature to pass a bill that would have nullified the judge's order, but the judge said no.
As introduced the bill strips away statutory language that requires the governor to call an election "as promptly as possible".
"Gov. Walker and legislative Republicans are so desperate to maintain their grip on power that they are changing laws to silence voters", said Jennifer Shilling, a Democrat from western Wisconsin who leads the minority in the state Senate.
In a Thursday morning tweetstorm, the Republican governor blamed "liberals from Washington, D.C." and Holder, whose national redistricting group sued Walker to force him to schedule the races.
The Democratic Party in Door County says they have a candidate ready to go when needed, but would not specify whom.
Both Legislators retired in December of last year, almost a year before the next election.