MINNEAPOLIS — Minnesota Gov. Mark Dayton said Tuesday he believes all Americans should be able to keep existing insurance plans under the new federal health care law, another prominent Democrat adding pressure to the White House as it tries to manage criticism of its federal health care law.

Dayton stressed that he has little influence as governor over the decision. But, he said, “the president promised that if people like their current policy they could keep it.”

Former President Bill Clinton also expressed that belief this week. He and Dayton have been among the many Democrats to strongly support the law. A White House spokesman said Monday the administration is looking at a range of options but said only small numbers of Americans are affected.

Still, Dayton described the number of people potentially affected in Minnesota as “staggering.”

The Minnesota Council of Health Plans has said about 140,000 Minnesotans have received letters from insurance companies telling them their plans could be substantially changed (Minnesota has a law against outright cancellation of policies). The total number of people affected is likely higher, since many plans cover more than one person.

Using the example of a 56-year-old man who’d be forced to pay for maternity coverage, Dayton said forcing people to pay for aspects of coverage they don’t need “defies common sense.”

Dayton also said he thinks that if technological delays continue to hamper the pace of enrollment in health insurance exchanges, that the administration should consider delaying the date at which Americans are financially penalized for not having health insurance. That’s currently planned for mid-March. Dayton stressed, as he has repeatedly, that he believes Minnesota’s health insurance exchange is a success so far particularly in relation to its troubled federal counterpart.

Dayton spoke Tuesday to the Minnesota Medical Association. Dr. Jeremy Springer, a family physician and administrator at Park Nicollet Medical Center in St. Louis Park, said many Minnesota physicians are worried about the potential flood of new patients that could come starting Jan. 1 when new coverage kicks in.

“It’s still a huge unknown for a lot of us,” Springer said. Because the new law stresses preventative care, he said doctors are worried about strained resources.

“We’re still not sure who’s going to sign up, and where they’re going to go,” Springer said.