More Minnesotans would get help paying for college under DFL Gov. Mark Dayton’s $62 million plan to expand the state’s grant program for low- and middle-income students.

The proposal amounts to a small piece of the governor’s $46 billion, two-year budget proposal, which is now being considered by the state Legislature. But the governor’s office has singled it out as one of its major strategies to ensure that more students from a variety of backgrounds are able to attend and graduate from college — and that the state has enough trained workers for its growing number of jobs.

Lt. Gov. Tina Smith said the state projects having 100,000 more jobs than workers to fill those positions by 2020. But officials worry that the rising cost of college is keeping students from getting the training they need.

“More and more jobs are requiring higher education and career education, that education is costing more and people are either not finishing their degrees because it’s not affordable, or finishing with debt so high that for multiple years they are living paycheck to paycheck,” Smith said.

Speaking to reporters on Friday, Smith and Higher Education Commissioner Larry Pogemiller said the plan amounts to a 17 percent increase in the amount of money the state spends on grants. It would both provide more money to students who were already eligible for state grants and broaden the category of students and families who qualify for the assistance.

Grants would be available to students from households that make $35,000 to $85,000 per year. The students and their families would still be responsible for 50 percent of their college costs. But Pogemiller said an expanded program would help more people who fall between the cracks of education funding, making too much for federal grants but not enough to pay for college without help.

“It’s low income but also lower middle income,” he said. “That’s the group that’s taking on heavy debt now because many of them are not eligible for things like Pell Grants.”

Pogemiller said the additional funding would amount to about $775 per year for many students. Currently, about 82,000 to 84,000 students receive state grants.

The governor’s budget plan includes other proposals targeted at higher education, including $125 million for career readiness centers at Minnesota State campuses and $300,000 for a new effort aimed at reducing sexual assaults on college campuses. Money for new or expanded programs would come out of the state’s projected $1.4 billion surplus.

As the Legislature considers the grant proposal, a number of lawmakers have offered up their own plans. Bills introduced in the early weeks of the legislative session include proposals for student loan debt counseling and a loan forgiveness program.