North Carolina House Republicans are again proposing to modify their chamber's operating rules on veto overrides for the next two years, only now offering Democratic colleagues some broad limits on when they could be attempted.

Temporary House rules approved on a party-line vote last month omitted a rule from previous years that required chamber leaders to give at least two days’ notice before holding an override vote.

Democrats and left-leaning advocates criticized the rule's omission, which they said would allow Republicans to pick and choose when override attempts would occur during Democratic House members' brief floor absences, such as when taking a phone call or break.

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A proposal for permanent House rules filed Monday by House Rules Chairman Destin Hall doesn’t restore the previous rule. Instead, it states an override vote may be taken on the same day a veto message is received from Gov. Roy Cooper or from the Senate, or on "any other legislative day it is printed" on the chamber’s official agenda.

North Carolina Republicans are once again proposing modifications to veto override rules in the state Legislature.

With a 71-49 seat margin after the November elections, House Republicans fell one seat short of holding a majority large enough to override Democratic Gov. Cooper’s veto without needing support from Democrats. This balance of power could affect the outcome of bills on abortion, gun rights and immigration.

Moore had downplayed last month’s change, adding he wouldn’t "ambush" Democrats by taking a surprise vote.

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Hall, a Caldwell County Republican and a top lieutenant to Speaker Tim Moore, said in an interview that a floor vote was expected Wednesday on the permanent rules proposal. Some leading House Democrats received the proposal last week following discussions between the two sides, Hall said.

The override language is "a reasonable compromise," Hall said. "It certainly calms any fear from members about not having notice that a veto override (vote) is going to take place."

Based on the state constitution’s veto provisions, Republicans could succeed with an override if only two Democrats are absent and all Republicans are present. Senate Republicans already hold a veto-proof majority in their chamber.

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House Minority Leader Robert Reives of Chatham County said Monday he was aware of the permanent rules proposal but needed to "review its actual effect" before saying whether the Democratic caucus will support it. Enacting the rules only requires a simple majority, however.