ST. PAUL — Barely a month into his new job last winter, Gov. Mark Dayton got an unusual gift from a farmer visiting the Capitol: an acorn-sized stone with a cross-shaped marking that the farmer described as a good-luck charm.

The new Democratic governor accepted the gift, rubbed it and said: “Alright, I need good luck here.”

Nearly a year later, the supposed charm looks more like a rock. Dayton spent 2011 in nearly constant battle with equally new Republican legislative majorities, and ended the year with little to show for the aggravation.

The centerpiece of Dayton’s campaign for governor was a proposed income tax increase on the state’s wealthy, and once in office he directed much rhetorical energy toward pushing the plan. But he was finally forced to drop it when Republican lawmakers wouldn’t budge even in the face of a government shutdown. Dayton stuck his neck out as cheerleader-in-chief for partial state funding of a new Vikings stadium — but couldn’t get state lawmakers similarly enthused. He authorized a union election for some in-home child care workers, but a judge blocked the vote.

The year was not without victories. Dayton saved the state money with an executive order that snared federal aid by expanding Medicaid coverage for the poor. And his administration saved tens of millions more by striking a deal with health providers to limit their profits from publicly subsidized patients. He sped up state review of construction permits, part of a broad effort to make government more efficient that hijacked the issue from Republicans.

“I know that I did my very best,” Dayton told The Associated Press in an interview at his State Capitol office. “I didn’t accomplish all that I wanted to. I was dealing with a legislative majority that disagreed with my views on tax reform, on making the richest Minnesotans pay their fair share of taxes.”

Some of Dayton’s fellow Democrats said they wanted a little more fight from the state’s first Democratic chief executive in 20 years.

“He’s been too much of a pushover too often for the Republicans in his haste to compromise and be bipartisan,” said state Rep. Mindy Greiling, a Democrat from Roseville and a leading liberal voice in the party. “I would like him to hang tough longer.”

In particular, Greiling and many Democrats disdained the deal Dayton and GOP legislative leaders struck last July to balance the budget and end a 20-day partial government shutdown. It relied largely on delaying state aid payments to school districts, and borrowing on future proceeds from the state’s 1998 settlement with tobacco companies.

Dayton said he cut the deal after realizing even the government shutdown wouldn’t move Republicans off their no-tax-hikes mantra. “Compromise means agreeing to things that you don’t agree with,” he said.

Dayton, who will turn 65 at the end of January, is in the twilight of a career that’s centered on politics. He ran a state agency under the last Democratic governor, Rudy Perpich, and served single terms as state auditor and U.S. senator before finally winning a governor’s office that had eluded him on a previous try. He said he is already plotting his 2014 re-election campaign.

Dayton has not been shy about publicly lambasting Republican state lawmakers. “There are people there that view compromise as a weakness, not an asset,” he said.

But he’s also worked hard to build personal relationships with people in the opposing party.

Dayton has hosted legislators at the governor’s mansion 42 times, many for a meal. He’s gone fishing and hunting with the House speaker, and had his family over for dinner. Lawmakers of both parties came by the mansion for a Vikings viewing party earlier this month.

A week after chatting with Dayton at the mansion last winter, Republican Sen. Doug Magnus was invited to tag along on the governor’s plane for a business groundbreaking ceremony in his southwestern Minnesota district. The two traded stories about their families, interests and political pasts.

“He’s polite and he’s cordial. He’s a self-deprecating person,” Magnus said. “He’s not a highfalutin sort of fellow. That goes good with us down in the rural areas.”

Magnus, chairman of the Senate Agriculture Committee, sponsored the only budget bill to be signed before the shutdown. The duo, polar opposites politically, is now collaborating on stadium legislation.

Dayton, allies say, set out to be a doer and not just a glorified manager. During his campaign, Dayton fondly recalled Perpich for his big-think initiatives, which occasionally ran against Democratic Party orthodoxy. Some of Perpich’s ideas were viewed skeptically at first but left a lasting imprint, such as the first-in-the-country charter school law, which allowed high school students to earn college credits and state assistance to build a shopping palace known as the Mall of America.

Democratic Sen. Tom Bakk said the budget crunch constricted Dayton in his first year, but he thinks the governor is now looking for Perpich-like legacy proposals of his own.

“He wants to be remembered for some things. He may not know exactly what it is today yet,” said Bakk, who as Senate minority leader has worked closely with the governor. “He came into office at a time the state was in incredible crisis. He won’t be measured by his first year in office, I’m sure.”

For all of Dayton’s freshman bruises, conditions appear brighter as the calendar flips.

The budget outlook shows a slight surplus. Discussion of the Vikings stadium is intensifying, and the 2012 session includes little, if any, must-do work — meaning reduced chance of conflict the likes of which characterized year one.

Any disagreements between Dayton and GOP lawmakers can be taken to the fall election instead of resulting in another shutdown or similar catastrophe. Even though he won’t be on the November ballot, Dayton plans to aggressively campaign to elect Democratic legislative majorities that can aid his policy goals. He has already been laying the groundwork for an overhaul of the state tax code in the 2013 legislative session. Particularly if Democrats can regain legislative control, he has vowed to push once again for his much-desired income tax increase on the wealthy.

Today, the rock from that farmer sits on the desk of one of Dayton’s closest aides, press secretary Katharine Tinucci. Said the governor: “I give things to her when I want to be sure I don’t lose them.”