In Colorado, a state where voters outlawed same-sex marriage a half-decade ago and Republican voters outnumber Democrats, Democrats swept to full control of state government in 2012. Over the last year, they have enacted sweeping changes on gun control, marijuana legalization and civil unions. Some of the legislation has provoked a fierce reaction from voters: Two Democratic state senators who supported the gun-control bill were ousted in recall elections in September, while a third recently resigned to avoid being forced into a recall vote.

“There’s undoubtedly more interest in what’s happening in the states right now,” said Michael Sargeant, executive director of the Democratic Legislative Campaign Committee, which raised significantly more money in 2012 than in any previous cycle since its founding. “There is less of a knee-jerk need among some donors that their contributions need to stay in their state.”

This year, Republicans are targeting states like West Virginia. The state has long been reliably Democratic, but disputes over the regulation of coal mining and environmental rules have alienated important Democratic constituencies, providing what Republicans believe is a clear chance to flip the state Republican over the next few election cycles.

Charles and David Koch, brothers whose philanthropic and political network has helped fuel a Republican resurgence in the onetime union strongholds of the industrial Midwest, have also stepped up their political activity in the states; they hope to rebound in places like Virginia, where a Democrat won the governorship in 2013, and consolidate earlier victories in states like Michigan and Wisconsin.

Liberal donors are following suit, focusing on states like Arizona, where Latino immigration has expanded the pool of potential Democratic voters. Last spring, the Democracy Alliance began a $10 million State Initiatives Fund, aimed at building liberal organizations and winning back legislative seats in 12 states, including North Carolina and Florida. In Maine, a consortium of progressive groups financed by the hedge fund billionaire S. Donald Sussman, an alliance member, is looking to unseat Gov. Paul R. LePage this year and put both the governor’s office and the Legislature under Democratic control.

In a measure of their ambition, liberal groups are even targeting some states in the Old South, convinced that superior organization and money can help them begin to win back governorships and legislative seats. Interest has focused on Georgia, which has experienced significant Latino immigration and where 600,000 voting-age African-Americans are not yet registered to vote.

Last year, there were fewer Democrats on the ballot in Georgia than in any year on record, according to Bryan Long, the founder of Better Georgia, a liberal group. In recent months, Mr. Long — inspired by states like Minnesota — has circulated proposals to labor leaders and to donors in Georgia and around the country to build a $5 million political infrastructure for nonprofit groups, outside the traditional party organization.

“We’ve seen huge wins in other states,” Mr. Long said. “And here in Georgia, we’ve learned what’s possible: If you fight back, you win. And if you fight smart, you win more.”