Instead of imposing higher co-pays and rolling back health insurance coverage for state employees, Connecticut officials want their workers to get a colonoscopy to help cut costs.

v. Dannel P. Malloy on Thursday gave his negotiators and union leaders more time to discuss $2 billion in labor savings, putting off — for now — issuing the threatened first round of layoff notices to about 4,000 Connecticut workers a day before they were to go out.

The Republican leaders of the Connecticut General Assembly called on Democratic Gov. Dannel P. Malloy Thursday to support their efforts to end the practice of making payments for longevity on the job to certain veteran state employees.