A group of Democratic governors backed off from a last-minute effort to urge the Reagan administration to reduce unemployment and the huge federal budget deficit after Republicans criticized the plan as too partisan.

Michigan Gov. James Blanchard (D), enlivening a routine final session of the National Governors' Association, complained that his colleagues had failed to take a stand against the projected $200 billion deficit that has dominated all economic discussions here. Blanchard said the high level of federal borrowing "could choke off any economic recovery and not allow us to get people back to work."

But Republicans, led by Illinois Gov. James R. Thompson, who became the association's new president today, balked at suggestions that they endorse a critical Democratic resolution on the economy. Republican Gov. Christopher Bond of Missouri said that when he saw the Democratic resolution, "I could neither approve it nor stomach it."

The Democrats, who enjoy a 34-to-16 majority, had the votes to push through the resolution, but they elected not to shatter the group's fragile bipartisan consensus, particularly as the presidential campaign draws closer.

The dispute was more over style than substance. The governors' conference urged Congress last February to reduce the deficit by raising taxes, holding down defense spending increases and cutting the largest entitlement programs.

The Democratic statement was less specific. It called for a greater emphasis on unemployment and said the administration's "massive federal budget deficits . . . have had the effect of favoring the wealthy and have placed undue hardships upon the working people of this nation."

Blanchard eventually withdrew the proposal. But Thompson said later he would tell President Reagan at a meeting next month that the governors remain committed to seeing the deficit cut and that the problem cannot wait until after the 1984 election.

The governors did approve an amendment by Ohio Gov. Richard F. Celeste (D) that urges Congress to extend a 16-week program of supplemental unemployment benefits beyond its scheduled expiration on Sept. 30. The amendment also asked Congress to defer interest charges on states that have borrowed from the federal unemployment fund, an expense that is now costing Ohio $321,000 a day.