Sen. Dick Lugar (R-Ind.) began 2011 with more than $2 million in the bank and Sen. Ben Nelson (D-Neb.) had more than $1 million, according to year-end fundraising reports that began to trickle in ahead of Monday’s filing deadline.

Lugar, who is expected to face a tea-party-backed challenger in the Republican primary, had $2.4 million on hand at the end of December. Lugar has not had a competitive race in years, but he has said he’s running for re-election and has already been holding fundraisers this year. Tea party leaders in Indiana hope to rally around one candidate to oppose him.

The top Republican on the Senate Foreign Relations Committee was first elected in 1976. He was unopposed in the 2006 Republican primary and had no Democratic opponent that year.

Roll Call Politics rates the Indiana Senate race Likely Republican.

Nelson, meanwhile, is considered the most vulnerable incumbent up for re-election in 2012. He had $1.5 million on hand at the end of 2010, a sum that could go far in a relatively inexpensive state.

Nelson has already attracted a top-tier GOP challenger in Nebraska Attorney General Jon Bruning, and the conservative American Future Fund is running a radio ad against him. The Senator ran his first ad of the 2012 election cycle before the 2010 elections even took place.

Roll Call Politics rates the Nebraska Senate race a Tossup.

Earlier this week, Sen. Olympia Snowe (R-Maine) reported she had $1.2 million on hand as of Dec. 31. Snowe, like Lugar, faces more competition in the GOP primary than in the general election. The tea party has also indicated it wants to find a challenger to Snowe.

Year-end fundraising reports are due to be postmarked by midnight Monday, providing the first glimpse of the financial health of the 33 Senators who are up for re-election in 2012.

Erin Mershon and Mackenzie Weinger contributed to this report.