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For his part, Mr. McAuliffe recently said on WTOP’s “Ask the Governor” program that the only ones talking about a government shutdown in Virginia are House Republicans.

But House Majority Leader M. Kirkland Cox, Colonial Heights Republican, said Tuesday that Mr. McAuliffe can send down any proposal he wants and the body would gladly debate it — just not under the current circumstances.

“We are willing to have that debate, but not with the threat of a government shutdown looming,” he said.

If the two sides cannot agree, they run the risk of a shutdown once the new fiscal year starts on July 1.