The House on Wednesday voted 233-193 in favor of a $3.4 trillion, fiscal 2010 budget conference report, a strong show of support for President Barack Obama’s agenda as Democrats mark his 100th day in office.

Seventeen Democrats and 176 Republicans voted against the measure; no Republicans supported it. The original House budget plan passed 233-196 without Republican support.

The Senate is expected to follow suit later in the day.

The vote came after leaders in the fiscally conservative Democratic Blue Dog Coalition endorsed the plan yesterday. The Blue Dogs extracted promises from House leaders and Obama to abide by pay-as-you-go budget rules in the future, but failed to get Senate leaders to go along.

The spending blueprint also clears the way for overhauls of health care and student loans by including fast-track instructions. Those rules, known as reconciliation, would allow bills to pass the Senate with just 51 votes instead of the 60 usually needed to end debate.

Democratic leaders had argued reconciliation would prevent Republicans from holding their top priorities hostage, but with the defection Tuesday of Sen. Arlen Specter (Pa.) to the Democratic ranks and the likely seating of Democrat Al Franken as the junior senator from Minnesota, the rules would instead prevent the party’s conservative wing from blocking those bills.

Democrats have said they will try to move legislation without using the hardball reconciliation tactic before Oct. 15, when the rules would kick in. They also have argued that the rules will encourage Republicans and their fellow Democrats to negotiate on issues like health care.

Although the budget plan trims Obama’s spending requests, the resolution still calls for a significant increase in spending on top of the already-enacted $787 billion economic stimulus package, and it presumes a record-breaking increase in the national debt.