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Still, many observers see a trend in favor of Republicans.

“If a Republican can win in a fairly high-turnout election … in Massachusetts, is there anywhere they can’t win?” analyst Sean Trende wrote on the Real Clear Politics Web site.

The emerging power of the tea party movement, which organized large, grass-roots demonstrations over the summer, combined with the populist message that put Mr. Brown into office, has changed the dynamic of this year’s midterm elections. The fact the Republicans are polling well in Democratic strongholds such as Wisconsin, New York and even Washington state — where the only poll taken so far shows Sen. Patty Murray leading by just two percentage points — has worried some Democrats.

“In the wake of [Mr. Brown’s] win in Massachusetts, a notable proportion — 45 percent — of registered Democratic voters in New York state say they are worried that a Republican will defeat the state’s Democratic senators running for office in November,” the New York Marist poll said.

Other states are also newly in play. In Indiana, two-term Sen. Evan Bayh finds himself in a tightening race. The latest Rasmussen poll showed Mr. Bayh, a moderate Democrat who voted for President Obama’s health care overhaul bill, trailing Republican Rep. Mike Pence by three percentage points. Mr. Pence last week decided not to run, but other Republicans are lining up to take on Mr. Bayh, who is polling at less than 50 percent against two other possible Republican challengers.

Another Democratic seat now in play is Mr. Obama’s former seat in Illinois. His appointed replacement, Roland W. Burris, is not seeking election, and polls ahead of Tuesday’s primary showed moderate Republican Rep. Mark Steven Kirk, a Navy reservist who recently returned from a deployment to Afghanistan, running strongly against any likely Democratic opponent.

The political atmosphere in Colorado also has changed sharply. The latest poll by Daily Kos, a liberal Web site, gave a one-point edge to freshman Sen. Michael Bennet, a Democrat, but recent polls by Rasmussen show former Lt. Gov. Jane Norton, a Republican, with a 12-point lead over the incumbent.

Some analysts said that turning the Senate contests into a vote of confidence on the Democratic majorities in Congress could be a winning strategy this fall for the Republicans, especially among independents.

“The best thing the GOP can do is to keep the election as a referendum on the Democrats, rather than a choice between the parties,” said pollster Scott Rasmussen. “Unaffiliated voters voted against the party in power during 2006 and 2008. They did so again in 2009, and appear poised to do so in 2010.”

Mr. Zogby said Republicans “are at the mercy of the economy.”

“If there is any uptick in employment or other key indicators, the administration can claim success,” he said.

On Monday, the Obama administration predicted little improvement in the nation’s job situation. The forecast was a 9.8 percent unemployment rate at the end of this year, down only slightly from the current rate of 10 percent.

Even if Republicans do not take back control of the Senate this year, the outcome could serve them well.

“I’m not sure that Republicans want to win control in 2010,” Mr. Rasmussen said. “It would probably be better for them to get close in this cycle and leave the Democrats on top heading into 2012. The Senate lineup that year will give Republicans plenty of opportunities.”