Gov. Mark Dayton signed his first bill of the new legislative session last week, a $21 million tax cut package. This week he could be asked to sign a second, but it’s less likely to end quickly with the kind of cheery news conference that went with the tax-bill signing.

Republicans succeeded last week in passing health care premium relief through the Senate and aim to follow this week with a similar vote in the House. Dayton shares Republicans’ goal of helping the approximately 123,000 Minnesotans who buy insurance on the individual market and have seen their premiums soar by 50 percent or more, but has a plan of his own.

If the House passes its bill, members from that chamber and the Senate will meet in conference to refine a single bill to send to the governor. But if Republicans don’t make some adjustments to the bill, Dayton has warned he could veto it.

Dayton said last week that he would not sign a bill that includes “reinsurance,” a $150 million provision tucked into the Senate bill intended to bolster the individual market by helping insurance companies weather the costs of people with extraordinarily high health care expenses. He’s also concerned about the way the GOP bill would distribute about $300 million in premium rebates through the state, a process his budget officials have said could cost $20 million and take a year to complete.

The governor continues to push for the $313 million plan he introduced in October, which would offer 25 percent premium rebates issued directly through insurers, in the form of smaller bills.