HARTFORD, Conn. >> United Technologies Corp. says it may furlough more than 5,000 workers if the U.S. government shutdown continues into next month.

The company said today that its Sikorsky division, which makes Black Hawk helicopters, would be hit first. It expects nearly 2,000 employees, including those employed at facilities in Connecticut, Florida and Alabama, will be furloughed on Monday.

The Hartford, Conn.-based manufacturer said it would halt some defense manufacturing because government inspectors themselves have been furloughed. That leaves it without the necessary federal approvals to make military products.

If the shutdown continues through next week, the furloughs would extend to its Pratt & Whitney and UTC Aerospace Systems division, bringing the total number of employees on hold up to 4,000. That number could exceed 5,000 if the shutdown stretches into next month.

United Technologies employs about 218,300. Of its annual revenue of $57.7 billion in 2012, $10.1 billion came from the U.S. government.

“This is what happens when House Republicans decide that political gamesmanship is more important than people’s jobs,” Connecticut’s Gov. Dannel P. Malloy, a Democrat, said. “It’s unconscionable that so many working families would be unfairly put in this situation.”

Members of Connecticut’s Democratic Congressional delegation also called for House Republicans to end the budget impasse.

“These wounds are tragically self-inflicted and dramatize the cumulative and increasing destructive economic effects of the shutdown,” said Sen. Richard Blumenthal.

U.S. Rep. Rosa DeLauro, whose district includes Sikorsky’s headquarters, said, “The political games must end to keep these hardworking men and women on the job, prevent further pain for working families and end the damage it is inflicting on our economy.”

The partial government shutdown, which took effect Tuesday, has idled roughly 800,000 “non-essential” federal workers.

United Technologies’ stock fell $2.40 to close at $104.98 today.