Republicans suspect last year's votes are one of the reasons why Obama has pushed back the release of his budget plan to early April. The delay has already been criticized by Republicans as an example of failed leadership on the part of Obama, but it will also spare the administration from another potentially ugly vote.

However, there is already some talk that Senate Republicans will try to force the issue by forcing a vote on the Obama budget once it comes out.

GOP aides also say Obama's late budget is also a likely tactical move designed to avoid additional scrutiny about the budget in general, especially as Senate Democrats are looking to move their first budget plan in four years.

The Democratic budget has already come under heavy fire from Republicans who say it over-estimates the extent to which it would reduce the deficit, and raises $1 trillion in new taxes. Democrats say it cuts the deficit by $1.85 trillion over ten years, but the GOP has said that because it assumes the sequester will not happen, the amount if deficit reduction is closer to $700 billion.

In contrast, Republicans are proposing a balanced budget in 10 years that gets there by reducing the rate of growth in government spending, and includes $5.7 trillion in deficit reduction and no new taxes. The combination of slower growth in spending and the repeal of the 2010 healthcare law has led to ongoing Democratic criticism.

Both the House and Senate are looking to move budget plans this week. The Senate's plans for consider the Democratic budget and possibly others are expected to become more clear early this week.

Last year, the Senate rejected all five budget plans that its members were presented, including the House GOP budget, which failed 41-58.

In the House, the Rules Committee will meet at 5 p.m. today to establish a rule for the budget plan from Budget Committee Chairman Paul RyanPaul Davis RyanDems: Ryan ‘sole impediment’ to DACA deal The Hill's 12:30 Report The Hill's Morning Report: Haley clashes with White House MORE (R-Wis.). As usual, the House is expected to consider several other budget alternatives, which are expected to fail before passage of Ryan's budget.

Last year, the House considered six additional budget plans, all of which were rejected. They were from the Congressional Black Caucus (failed 107-314), a bipartisan group that recommended a Bowles-Simpson-based plan (failed 38-382), the Progressive Caucus (failed 78-346), the Republican Study Committee (failed 136-285), the mainstream Democrats (failed 163-262), and a plan presented by Republicans based on Obama's budget (failed 0-414).

Budget Committee ranking member Chris Van Hollen (D-Md.) is expected to announce the main Democratic budget plan this afternoon.

— Erik Wasson contributed